what is the voltage reading vr(t) given by the voltmeter across the resistor (figure 2) at time t after t

(1a) The potential energy of the body is 980 J

(1b) The kinetic energy of the body halfway down is 490 J and

(1c) The kinetic energy just before impact is 9807 J.

(2) The work done by the trailer on the car is 15,750,000 J.

(3)The initial speed of the vehicle was 10.6 m/s and the work required to stop the car is 269.9 kJ.

Problem 1:

The potential energy of the body is given by the formula:

potential energy = mass x gravity x height

where mass = 50 kg, gravity = 9.8 m/s², and height = 2 m

So, potential energy = 50 x 9.8 x 2 = 980 J

When the body is halfway down, its height above the ground is 1 m. At this point, the potential energy is:

potential energy = mass x gravity x height

potential energy = 50 x 9.8 x 1 = 490 J

The total energy of the body (at any point) is the sum of its potential energy and kinetic energy.

Therefore, the kinetic energy of the body halfway down is:

kinetic energy = total energy - potential energy

kinetic energy = (50 x 9.8 x 2) - (50 x 9.8 x 1) = 490 J

Just before impact with the floor, the height of the body above the ground is zero, so the potential energy is also zero.

At this point, the total energy of the body is equal to its kinetic energy:

kinetic energy = (1/2) x mass x velocity²

where mass = 50 kg, and velocity = ?

To find the velocity, we can use the conservation of energy principle:

total energy at the top = total energy just before impact

potential energy at the top = kinetic energy just before impact

potential energy at the top = 50 x 9.8 x 2 = 980 J

kinetic energy just before impact = 980 J

So, (1/2) x 50 x velocity^2 = 980 J

Solving for velocity, we get:

velocity = √(2 x 980 / 50) = 19.8 m/s

Therefore, the kinetic energy just before impact is:

kinetic energy = (1/2) x 50 x (19.8)^2 = 9,807 J

Problem 2:

The work done by the trailer on the car is given by the formula:

work = force x distance

where force = 900 N, and distance = (70 km/h) x (15/60) h = 17.5 km

Converting km to meters, we get:

distance = 17.5 km x 1000 m/km = 17,500 m

So, work = 900 x 17,500 = 15,750,000 J

Problem 3:

The work done by the brakes is equal to the change in kinetic energy of the vehicle:

work done by brakes = change in kinetic energy

Let the initial speed of the vehicle be v m/s. Then, the initial kinetic energy of the vehicle is:

kinetic energy = (1/2) x 1600 x v²

After the brakes are applied, the final kinetic energy of the vehicle is zero (since the vehicle comes to a stop).

Therefore, the work done by the brakes is equal to the initial kinetic energy:

work done by brakes = (1/2) x 1600 x v²

Given that the work done by the brakes is 90 kJ, we can solve for the initial speed:

90,000 J = (1/2) x 1600 x v²

v² = 112.5

v = √(112.5) = 10.6 m/s

So, the initial speed of the vehicle was 10.6 m/s.

The work required to stop the car:

W = ¹/₂(1600)(15² + 10.6²)

W = 269,888 J = 269.9 kJ

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Answer:

Explanation:

According to the law of conservation of momentum, the total momentum before the collision must be equal to the total momentum after the collision. We can use this principle to determine the resulting velocity of Kaylyn's puck after the collision.

Before the collision, Sharon's puck has a momentum of:

p1 = m1 * v1 = 0.3 kg * 6 m/s = 1.8 kg m/s

where m1 is the mass of Sharon's puck and v1 is its velocity.

Kaylyn's puck is at rest before the collision, so its momentum is:

p2 = m2 * v2 = 0.3 kg * 0 m/s = 0

where m2 is the mass of Kaylyn's puck and v2 is its velocity.

After the collision, Sharon's puck is at rest, so its momentum is:

p1' = m1 * v1' = 0.3 kg * 0 m/s = 0

where v1' is the velocity of Sharon's puck after the collision.

The total momentum after the collision is the momentum of Kaylyn's puck:

p2' = m2 * v2'

where v2' is the resulting velocity of Kaylyn's puck after the collision.

Using the conservation of momentum principle, we can write:

p1 + p2 = p1' + p2'

Substituting the values we have calculated:

1.8 kg m/s + 0 = 0 + 0.3 kg * v2'

Solving for v2':

v2' = (1.8 kg m/s) / (0.3 kg) = 6 m/s

Therefore, the resulting velocity of Kaylyn's puck after the collision is 6 m/s, which is equal to the velocity of Sharon's puck before they collided. The correct answer is option A.

When the snow melts, it will form liquid water, and the volume of the water will be equal to the volume of the original snow sample. Therefore, the volume of liquid water produced by the melting of the 24 ml sample of snow is also 24 ml.

If the snow has a density of 0.5 g/ml, then the mass of the snow is:

mass = density x volume = 0.5 g/ml x 24 ml = 12 g

Therefore, the volume of liquid water produced by the melting of the 24 ml sample of snow is also 24 ml.

What is volume?

Volume of liquid refers to the amount of space that a liquid occupies. It is a measure of the three-dimensional space that the liquid occupies and is usually measured in units such as liters, milliliters, gallons, or fluid ounces. The volume of a liquid is determined by the shape of the container in which it is placed, and it can be measured directly using a graduated cylinder or other volumetric measuring device.

What is density?

Density is a physical property of matter that describes how much mass is present in a given volume of a substance. It is defined as the mass of a substance per unit volume, and is typically measured in units such as grams per milliliter (g/mL) or kilograms per cubic meter (kg/m³).

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Cleats or dogs are pieces of metal that are temporarily attached to the weldment’s parts to enable them to be forced into place. Anytime these pieces of metal are used, they must be removed, and the area around Smooth

In this case option D

Cleats or dogs are pieces of metal that are commonly used in welding to temporarily attach the parts of the weldment in place. They are typically small metal pieces with angled ends that can be clamped or welded onto the parts being joined to hold them in the correct position during the welding process.

Once the welding is completed, the cleats or dogs must be removed and the area where they were attached must be ground smooth.

This ensures that the final welded joint has a smooth and even surface and that there are no residual metal pieces that could interfere with the joint's structural integrity.

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Based on what you learned about the roller coaster ride, the following statements about energy transformations that are true are: A. Kinetic energy can be converted into several other types of energyC. A change in an object's speed is evidence that the object's kinetic energy is changing.

The process of energy transformation is the conversion of one form of energy into another. This term describes the scientific process by which energy, in various forms, is transformed to do work. Energy transformation occurs in every physical system in the universe.

Kinetic energy can be converted into several other types of energy.Kinetic energy is the energy of a moving object. The energy is converted into various types of energy, such as electrical and thermal energy, as a result of movement. In a roller coaster, kinetic energy is converted into potential energy as the train goes up the lift hill. The potential energy is converted back into kinetic energy as the train goes down the first drop.

A change in an object's speed is evidence that the object's kinetic energy is changing.Kinetic energy changes when an object's speed changes. If an object slows down, its kinetic energy decreases, while if it speeds up, its kinetic energy increases. On the roller coaster, as the train moves up and down the track, its speed varies, causing changes in its kinetic energy.

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Answer:

F.  The forces exerted by the meteor and the spacecraft on each other will be of equal strength.

A 30.0-kg box is being pulled across a carpeted floor by a horizontal force of 230 N , against a friction force of 210 N . The acceleration of the box is 0.667 m/s².

The acceleration of the box can be calculated using the formula:

acceleration = (Net force) / (mass)

The given values in the question are:

mass of the box = 30.0 kg

force applied on the box = 230 N

friction force acting on the box = 210 N

Now, let's calculate the net force acting on the box:

Net force = (force applied) - (friction force)= 230 N - 210 N= 20 N

Thus, the net force acting on the box is 20 N.

Using the formula mentioned above, the acceleration of the box can be calculated as:

acceleration = (Net force) / (mass)

                    = 20 N / 30.0 kg

                    = 0.667 m/s²

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The positions marked by the straight arrows in the image are the first quarter and third quarter phases of the Moon the tide that occurs is called a "neap tide".

What is neap tide?

During these phases, the Moon and the Sun are at right angles to each other with respect to the Earth, which causes the gravitational forces of the Moon and the Sun to partially cancel out. As a result, the tidal range is at its minimum, and the tide that occurs is called a "neap tide". Therefore, the answer is "neap".

What is gravitational forces?

Gravitational forces refer to the attractive force that exists between any two objects in the universe that have mass. This force is governed by Newton's law of universal gravitation, which states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

This means that the larger the mass of the objects, the stronger the gravitational force between them, and the farther apart they are, the weaker the gravitational force. Gravitational forces are responsible for keeping celestial bodies, such as planets, moons, and stars, in their orbits, and for the phenomena of tides on Earth caused by the gravitational pull of the Moon and the Sun.

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Complete question is: "neap tide" type of tide occurs when the moon is in the positions marked by the straight arrows in this image.

Answer:

(D)  the frictional force must be greater than the component of the gravitational force that acts down the ramp

The perimeter of the pool is approximately 206.85 feet if we use 3.14 as the approximation of the value of π.

In this case, the angle AOB is 360 degrees, so the arc length is:

arc length = (360/360) x 2π(25) = 50π feet

Finally, we can find the perimeter of the pool by adding up the lengths of the two semicircles and the arc AB:

perimeter = 2πr + 2r + arc length

perimeter = 2π(25) + 2(25) + 50π

perimeter = 50π + 50

Perimeter is a measurement of the distance around the edge of a two-dimensional shape, such as a square, rectangle, or circle. It is the sum of the lengths of all the sides that make up the shape. The perimeter is an important concept in geometry and is used to determine the amount of material needed to enclose or surround a shape, as well as to calculate the distance around a given route or path.

To find the perimeter of a shape, you simply add up the lengths of its sides. For example, if you have a square with sides that are each 5 units long, the perimeter would be 5 + 5 + 5 + 5 = 20 units. Similarly, if you have a circle with a radius of 10 units, the perimeter (also known as the circumference) would be 2πr or approximately 62.8 units.

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Complete Question: -

If AO is 50 feet, find the perimeter of the pool. (O is the center of the sector AOB. OA and OB are the diameters of two semi-circles.)

Answer:

Explanation:

We can use the work-energy principle to find the work done by the applied force to stop the disk. The work-energy principle states that the work done by all forces acting on an object is equal to the change in its kinetic energy:

W = ΔK

where W is the work done, and ΔK is the change in kinetic energy.

Initially, the disk is rotating with an angular velocity of 950 rev/min. We need to convert this to radians per second, which gives:

ω_initial = (950 rev/min) × (2π rad/rev) × (1 min/60 s) = 99.23 rad/s

The initial kinetic energy of the disk is:

K_initial = (1/2) I ω_initial^2

where I is the moment of inertia of the disk about its axis of rotation. For a uniform disk, the moment of inertia is:

I = (1/2) m R^2

where m is the mass of the disk, and R is the radius. Substituting the given values, we get:

I = (1/2) (190 kg) (1.1 m)^2 = 115.5 kg m^2

Therefore, the initial kinetic energy of the disk is:

K_initial = (1/2) (115.5 kg m^2) (99.23 rad/s)^2 = 565201 J

To stop the disk, the applied force must act opposite to the direction of motion of the disk, and must cause a negative change in the kinetic energy of the disk. The force is applied at a radial distance of 0.5 m, which gives a torque of:

τ = F r

where F is the magnitude of the force. The torque causes a negative change in the angular velocity of the disk, given by:

Δω = τ / I

The work done by the applied force is:

W = ΔK = - (1/2) I Δω^2

Substituting the given values, we get:

W = - (1/2) (115.5 kg m^2) [(F r) / I]^2

The force F can be eliminated using the equation for torque:

F = τ / r = (Δω) I / r

Substituting this into the equation for work, we get:

W = - (1/2) (115.5 kg m^2) [(Δω) I / r I]^2

= - (1/2) (115.5 kg m^2) (Δω / r)^2

Substituting the values for Δω and r, we get:

W = - (1/2) (115.5 kg m^2) [(F r / I) / r]^2

= - (1/2) (115.5 kg m^2) [(2 Δω / R) / (2/5 m R^2)]^2

= - (1/2) (115.5 kg m^2) (25/4) (2 Δω / R)^2

= - 90609 J

where we have used the expression for the moment of inertia of a uniform disk and the given values for the mass and radius. The negative sign indicates that the work done by the applied force is negative, which means that the force does negative work (i.e., it takes energy away from the system). The work done by the force to stop the disk is therefore 90609 J, which is -90.6 kJ (to two decimal places).

Answer:

both are only physical changes

Explanation:

Physical changes are changes that do not alter the identity of a substance.

The liquid soap is still liquid soap when mixed into water.

The dry ice is still dry ice when it changes state from solid to gas.

The answers to the questions are:

Operant conditioning is a type of learning in which behavior is modified by its consequences. It involves the association of a behavior with its consequences, either reinforcement or punishment.

Reinforcement is when a consequence strengthens or increases the likelihood of a behavior occurring again in the future.

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Answer:

Explanation:

R/^5*r^6 Ok so  then this is simple once u get the answer u need to use the given formula in order to plug in the numbres sorry .

So basically

12 x r^6(u must fill in the number s ) and then u need to do `13x14xr the answer and use the rest of the numbers in order to figure out the quantities of each side for the shape . Then ur answer would be the r^x + x = ???

So yeah hope this helped

I think

Kind of

K Thanks Bye

The equivalent capacitance of the combination is 2.2405 μF.

To find the equivalent capacitance of the combination, we can use the formula:

1/C = 1/C1 + 1/C2 + 1/C3

where C1, C2, and C3 are the capacitances of the three capacitors.

Plugging in the values, we get:

1/C = 1/5.2μF + 1/7μF + 1/9μF

1/C = 0.1923077 + 0.1428571 + 0.1111111

1/C = 0.4462759

C = 1/0.4462759

C = 2.2405 μF (rounded to 4 significant figures)

Therefore, the equivalent capacitance of the combination is 2.2405 μF.

A system's capacitance is its capacity to store an electric charge. The proportion of the electric charge held on a conductor to the difference in potential between the conductors is what is meant by this term.

The farad (F), which is equal to one coulomb per volt, is the unit of capacitance.

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From the given figure of the quadrupole, it is seen that option A is correct. In an electric circuit, charges move from the negative pole (terminal) to the positive pole (terminal) of a battery or power source.

In physics, a quadrupole is a type of electric or magnetic field with a specific configuration of poles or charges. A quadrupole consists of two sets of charges or poles that are aligned in opposite directions, with each set having two charges or poles of equal magnitude but opposite signs. The charges or poles can be either electric or magnetic, and they are separated by a fixed distance. Quadrupoles can be used to manipulate charged particles, such as ions, in various applications, including mass spectrometry, particle accelerators, and ion traps. In particular, quadrupole mass spectrometry is a widely used technique in analytical chemistry and biochemistry for identifying and quantifying small molecules and biomolecules.

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Answer:1st one 3N to the left to achieve equilibrium

2nd one 5N to the left to achieve equilibrium

3rd one 2N to the top to achieve equilibrium

4th one 2N to the top to achieve equilibrium

5th one 8N to the right to achieve equilibrium

Explanation:

Explanation:

dhifgjrgrkfgd jsjhdhdj

shdjdjdj

hsjdjdj

shsjej

At position 2, ion B falls. It is less deflected because it has a lesser mass than ions C, D, and E and the same charge as ion A.

A force perpendicular to the charged particle's velocity and the magnetic field's direction is applied when it reaches the magnetic field. The right-hand rule asserts that the palm will face the direction of the force if the thumb of the right hand points in the direction of the particle's velocity and the fingers point in the direction of the magnetic field. The particle's charge, velocity, and magnetic field intensity all affect how much force is generated.

Since all ions are moving at the same speed in this scenario, the force exerted on each ion is proportional to its charge to mass ratio. Ion B has the smallest mass of all the ions, so the least force and is least deflected of the ions, falling at position 2.

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A. The hockey puck moved at a constant speed away from Janine.

The hockey puck is in equilibrium as a result of moving at a steady pace. Dynamic equilibrium is the name given to this form of equilibrium. Hence, if the hockey puck is moving over the ice at a constant pace, it is in equilibrium.

There is no connection between velocity and speed; velocity is the direction that an object moves in. Velocity is the combination of speed and direction. Speed and velocity are very similar to each other.

The sum of the forces exerted on an object must be zero since, in accordance with Newton's first law of motion, an object moving at a constant speed experiences no net external force.

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Answer:

To solve this problem, we can use the equation for rotational motion:

Δθ = (1/2) α t^2 + ω0 t

where Δθ is the change in angle, α is the angular acceleration, t is the time, and ω0 is the initial angular velocity.

In this case, we know that the initial angular velocity is 0 (since the blade is at rest), the final angular velocity is 80.0 rev/s, and the number of revolutions is 240.0 rev. We can use these values to find the angular acceleration:

ωf = ω0 + αt

80.0 rev/s = 0 + α(240.0 rev)

α = 80.0 rev/s / 240.0 rev

α = 1/3 rev/s^2

Now that we know the angular acceleration, we can use the moment of inertia and the torque equation:

τ = Iα

where τ is the torque, I is the moment of inertia, and α is the angular acceleration.

Substituting the given values, we get:

τ = (1.41×10^-3 kg.m^2)(1/3 rev/s^2)

τ = 4.70×10^-4 N.m

Therefore, the net torque the motor must apply to the blade is 4.70×10^-4 N.m.

If an equal amount of heat energy is applied to all the substances at the same time, aluminum will heat up more quickly compared to the other substances.

What is Specific Heat ?

Specific heat is the amount of heat energy required to raise the temperature of a substance by a certain amount, usually one degree Celsius or one Kelvin, per unit mass of the substance. It is a physical property that determines how much energy is needed to change the temperature of a material. Different materials have different specific heat values, which can be used to predict how they will behave when heated or cooled.

Looking at the table, we can see that water has the highest specific heat capacity of all the substances listed, at 4.18 J/g°C. This means that it requires more energy to raise the temperature of water compared to the other substances. Therefore, if an equal amount of heat energy is applied to all the substances at the same time, water will heat up more slowly compared to the other substances.

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The initial elongation of the material described by the Maxwell model is given by the formula, initial elongation = [tex]F_0[/tex]/k.

The initial elongation value at t=0 for the material described by the Maxwell model is given by the formula, initial elongation = [tex]F_0[/tex]/k.

Here, k represents the spring constant of the material.

Let's understand this in detail.

The Maxwell model is a type of viscoelastic model that is used to describe the behavior of certain materials. It is made up of a spring and a dashpot in series.

The spring represents the elastic component of the material and the dashpot represents the viscous component of the material.

In this model, the deformation of the material depends on the applied force as well as the time duration for which the force is applied.

The formula to calculate the initial elongation of the material is given by:

initial elongation = [tex]F_0[/tex]/k

where [tex]F_0[/tex] is the force applied to stretch the material and k is the spring constant of the material. The spring constant of a material is defined as the amount of force required to stretch the material by one unit.

The initial elongation of the material is calculated using the spring constant of the material. The spring constant represents the amount of force required to stretch the material by one unit.

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Answer:

Explanation:

The work-energy theorem states that the net work done on an object is equal to its change in kinetic energy. Therefore, we can use this theorem to calculate the final kinetic energy of the ball in each case.

We know that the work done by a constant force is given by the equation W = Fd cos(theta), where F is the magnitude of the force, d is the displacement of the ball, and theta is the angle between the force and displacement vectors.

Using the work-energy theorem, we can write:

W = ΔK = Kf - Ki

where ΔK is the change in kinetic energy, Kf is the final kinetic energy, and Ki is the initial kinetic energy.

We can rearrange this equation to solve for Kf:

Kf = Ki + W = Ki + Fd cos(theta)

a) Kf = 150 J + (10 N)(15 m)cos(90°) = 150 J

b) Kf = 300 J + (200 N)(1.5 m)cos(180°) = 0 J

c) Kf = 200 J + (25 N)(4 m)cos(0°) = 300 J

d) Kf = 450 J + (15 N)(30 m)cos(150°) = 112.5 J

Ranking from greatest to least final kinetic energy:

c) Ki=200J F=25N d=4m theta=0 degrees

a) Ki=150J F=10N d=15m theta=90 degrees

d) Ki=450J F=15N d=30m theta=150 degrees​

b) Ki=300J F=200N d=1.5m theta=180 degrees

the given values, we get va = sqrt((350 kg * 9.81 m/s² - 0)))

Since the cable is inextensible, the distance moved by both blocks is the same.

Let's denote the distance moved by both blocks as "d". Then, the distance moved by block A is "1m + d" to the right.

Using conservation of energy, we can write:

(1/2) * ma * va² + (1/2) * mb * vb²= (ma + mb) * g * d

where ma and mb are the masses of blocks A and B, va and vb are their velocities, and g is the acceleration due to gravity.

Since the system is released from rest, va = 0, and we can solve for vb:

(1/2) * mb * vb²= (ma + mb) * g * d

vb²= 2 * (ma + mb) * g * d / mb

vb = sqrt(2 * (ma + mb) * g * d / mb)

Now, we need to find the velocity of block A after it has moved 1m + d to the right. To do this, we can use the equations of motion. Since block A is moving to the right, we take the positive x direction to be to the right. Then, we have:

ma * a = T - fa

where a is the acceleration of block A, T is the tension in the cable, and fa is the frictional force acting on block A due to the incline.

The tension in the cable is the same throughout, so we can write:

T = mb * g

The frictional force fa can be calculated using:

fa = µ * ma * g * cos(theta)

where µ is the coefficient of friction, theta is the angle of the incline, and cos(theta) = 1/sqrt(2) since the incline makes a 45 degree angle with the horizontal.

Substituting these values, we get:

ma * a = mb * g - µ * ma * g / sqrt(2)

Solving for a, we get:

a = (mb * g - µ * ma * g / sqrt(2)) / ma

Now, we can use the equations of motion again to find the final velocity of block A after it has moved 1m + d to the right. We have:

d = (1/2) * a * t²

where t is the time taken by block A to move 1m + d to the right.

Substituting the value of a, we get:

d = (1/2) * [(mb * g - µ * ma * g / sqrt(2)) / ma] * t²

Solving for t, we get:

t = sqrt(2 * d * ma / (mb * g - µ * ma * g / sqrt(2)))

Finally, we can use the equations of motion again to find the final velocity of block A. We have:

1m + d = (1/2) * a * t²

Substituting the values of a and t, we get:

1m + d = (1/2) * [(mb * g - µ * ma * g / sqrt(2)) / ma] * [2 * d * ma / (mb * g - µ * ma * g / sqrt(2))]²

Solving for the final velocity of block A, we get:

va = sqrt((mb * g - µ * ma * g / sqrt(2)) / ma * (1m + d) / 2)

Substituting the given values, we get:

va = sqrt((350 kg * 9.81 m/s² - 0

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Using the triangle of forces to get the system of the forces;

If three forces acting on a body are in equilibrium, then they can be represented in magnitude and direction by the three sides of a triangle taken in order.

In other words, the three forces can be drawn as vectors, and these vectors can be arranged to form a closed triangle.

We know that we have the other end of the triangle to be;

100 Kg * 10 m/s^2 = 1000 N

The missing angle is;

180 - (30 + 60)

= 90 degrees

Thus;

1000/Sin 90 = T1/Sin 60

T1 = 100 Sin 60/Sin 90

T1 = 866/1

T1 = 866 N

1000/Sin 90 = T2/Sin 30

T2 = 1000 Sin 30/Sin 90

T2 = 500 N

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The number of earths that could fit  inside Jupiter is 6000 where the radius of Jupiter is 71492 km.

Given the volume of a sphere is (V) =[tex](4/3)*\pi*R^3[/tex]

The radius of Jupiter is (RJupiter) = 71492 km

Then the volume of Jupiter is (VJupiter) = [tex](4/3)*\pi*(71492)^3[/tex]

VJupiter = [tex]6.6 * 10^{15} km^3.[/tex]

We know the radius of earth = Re = 6371km

Then the volume of earth (Ve) =[tex]4/3 * \pi * (6371)^3[/tex]

Ve =  [tex]1.08 * 10^{12} km^3.[/tex]

Let the number of earths that could fit inside Jupiter = n

Therefore, n = VJupiter/VEarth

n = [tex]6.6 * 10^{15} km^3/1.08 * 10^{12} km^3 = 6 * 10^3[/tex], = 6,000 Earths.

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To solve problem 5.39, we first need to calculate the total torque applied to the shaft. To do this, we need to calculate the torques due to the distributed and concentrated loadings. The torque due to the distributed loading can be calculated as.

T_d = (2*pi*r*F_t*L)/2

where T_d is the torque due to the distributed loading, r is the radius of the shaft (56/2 = 28mm), F_t is the distributed load (N/m), and L is the length of the shaft.The torque due to the concentrated loading can be calculated as:

T_c = F_t * r where T_c is the torque due to the concentrated loading and F_t is the concentrated force (N).

Therefore, the total torque applied to the 56mm diameter solid shaft is: T_total = T_d + T_c

Here is the solution to problem 5.39:Given: Diameter of shaft, d = 56mmMaximum shear stress, τmax = 75 MN/m²Twist of shaft, φ = 2°Distributed torque, Td = 100 Nm Concentrated torque, Tc = 150 NmLength of shaft, L = 2mFrom the given data we have to calculate: Power transmitted by shaft Maximum shear stress in shaftAngle of twist per metre of shaft Maximum shear stress:

The maximum shear stress can be calculated by the formula,Tmax = 16Td/πd³ + 2Tc/πd³Let's substitute the values,Tmax = 16(100)/π(56)³ + 2(150)/π(56)³Tmax = 33.66 MN/m²Power transmitted by shaft:Power transmitted by shaft is calculated by the formula,P = TωWhere, T = torqueω = angular velocityLet's first calculate the angular velocity,Angular velocity, ω = 2πN/60Where, N = RPMSubstitute the given values and calculate,ω = 2π(300)/60ω = 31.42 rad/sPower transmitted by shaft,P = TωLet's calculate torque,Total torque, T = Td + Tc = 100 + 150 = 250 NmNow, substituting the values, we get,P = 250 × 31.42P = 7855.5 WP = 7.86 kW

Angle of twist per metre of shaft:Angle of twist per meter is calculated by the formula,ϕ/L = T/(JG)Where,T = torqueJ = polar moment of inertia of shaftG = modulus of rigidityLet's calculate J and G, for solid shaftJ = πd⁴/32G = τmaxLet's substitute the values and calculate,J = π(56)⁴/32J = 2.4856 × 10⁸ mm⁴G = 75 × 10⁶ N/m²G = 75 × 10⁶ mm²/s²Let's substitute the calculated values and calculate,ϕ/L = T/(JG)ϕ/L = 250/(2.4856 × 10⁸ × 75 × 10⁶)ϕ/L = 1.76 × 10⁻⁶ rad/mmTherefore, the angle of twist per meter is 1.76 × 10⁻⁶ rad/mm.

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The angular speed of the Frisbee is 21.33 rad/s.

What is Angular speed ?

Angular speed is a measure of how fast an object is rotating or moving around a central point or axis. It is a scalar quantity, which is defined as the rate of change of the object's angular displacement over time, expressed in units of radians per second (rad/s).

Angular speed is calculated using the formula:

Angular speed (ω) = Δθ / Δt

The linear speed of the outer edge of the Frisbee is given by:

v = 3.2 m/s

The diameter of the Frisbee is given by:

d = 30 cm = 0.3 m

The radius of the Frisbee is half the diameter:

r = d/2 = 0.15 m

The linear speed of a point on the edge of a rotating object is related to the angular speed by the formula:

v = ωr

where ω is the angular speed in radians per second.

Substituting the given values, we can solve for ω:

ω = v/r

ω = 3.2 m/s / 0.15 m

ω = 21.33 rad/s (rounded to two decimal places)

Therefore, the angular speed of the Frisbee is 21.33 rad/s.

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The final velocity of the combined mass after the collision is 15 m/s to the right.

This can be calculated using the equation for Conservation of Momentum.

The momentum of the combined mass before the collision is the sum of the momentums of the truck and car individually:

Momentum of Truck = 2000kg x 10 m/s = 20000 kgm/s

Momentum of Car = 500 kg x 20 m/s = 10000 kgm/s

Total Momentum before Collision = 30000 kgm/s

The total momentum after the collision is the same as before, so the final velocity of the combined mass is:

Final Velocity = Total Momentum/Combined Mass

Final Velocity = 30000 kgm/s / 2500 kg

Final Velocity = 15 m/s

therefore, the final velocity is 15 m/s.

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