A car traveling at 20 m/s runs into a bridge abutment and crumples for 1.2 m before coming to a full stop. If we estimate the process as constant deceleration motion, what is the average force exerted on the car, which weighs 1500 kg, during the collision process

Answer:

Accurate

Explanation:

Accuracy deals with the nearness of the measured values to the true value.

Precision is the ability to reproduce a certain result in a repeated fashion.

The reading is not precise because, the same weight is not reproduced. Different values of weight was reported from each of the measurement process.

Answer:

By a factor of 2

Explanation:

The angular displacement would change by a factor of 2.

The angular acceleration is represented by the formula

α = Δw / Δt, where

α = angular acceleration

Δw = change in velocity.

Δt = change in time taken

The angular displacement is given by the relation

s = rθ

s = arc length

r = distance

θ = angular displacement

We all know that velocity is the ratio of displacement and time, thus,

v = s/t

Angular acceleration on the other hand says that

α = w/t, substitute w for v, we have

α = s/t ÷ t

α = s/t * 1/t

α = s/t²

We see here that multiplying the acceleration by 2 will only be balanced by increasing the displacement by the same number, 2 in this case

Answer:

 F = mg /μ

Explanation:

For this exercise we define a coordinate system with the horizontal x axis and the vertical y axis, let's write the equilibrium equations for each axis

X axis

         F -N = 0

          F = N

Y axisy

         fr - W = 0

         fr = W                (2)

the force and touch have the expression

           fr = μ N

we substitute

          fr = μ F

we substitute in 2

         μ F = m g

          F = mg /μ

Answer: .36 m

Explanation:

The distance that the force is exerted over is equal to 0.3625 meter.

Given the following data:

To calculate the distance that the force is exerted over, we would apply the law of conservation of energy.

According to the law of conservation of energy, the work done by an external force equals the change in kinetic energy for the motion of the tennis ball hit by the racket.

Mathematically, this is given by this expression:

[tex]Work\;done = \Delta K.E = Fd[/tex]

Where:

Substituting the given parameters into the formula, we have;

[tex]29 = 80 \times d\\\\d=\frac{29}{80}[/tex]

Distance, d = 0.3625 meter.

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Answer:

[tex]L^2(\dfrac{8m}{3}+m_r)[/tex]

Explanation:

m = Mass of each rod

L = Length of rod = Radius of ring

[tex]m_r[/tex] = Mass of ring

Moment of inertia of a spoke

[tex]\dfrac{mL^2}{3}[/tex]

For 8 spokes

[tex]8\dfrac{mL^2}{3}[/tex]

Moment of inertia of ring

[tex]m_rL^2[/tex]

Total moment of inertia

[tex]8\dfrac{mL^2}{3}+m_rL^2\\\Rightarrow L^2(\dfrac{8m}{3}+m_r)[/tex]

The moment of inertia of the wheel through an axis through the center and perpendicular to the plane of the ring is [tex]L^2(\dfrac{8m}{3}+m_r)[/tex].

Angle of projection of the dart = 60°

initial velocity of the dart = 14.1 m/s

Using basic trigonometry, we can see that:

Vertical component of the Dart = 14.1*Sin 60° = 12.2 m/s

Horizontal component of the Dart = 14.1*Cos 60° = 7.05 m/s

Explaining the concept:

Once the dart is in mid-air, there will be no force that will reduce its horizontal velocity

So, the dart will be moving at a constant horizontal velocity of 7.05 m/s

but the force of gravity will be applied on the dart while mid-air and will pull it downwards with an acceleration of 9.8 m/s²

Hence, the time the dart will be aloft is the same as the time taken by the dart to reach the ground if we threw it vertically upwards at a velocity of 12.2 m/s

Solving for the time taken for the dart to reach the ground:

initial velocity = 12.2 m/s          

velocity at max height = 0 m/s      

acceleration = -9.8 m/s

time taken to reach max height:

v = u + at            using the first equation of motion

replacing the variables

0  = 12.2 + (-9.8)t

t = -12.2 / -9.8

t = 1.24 seconds

Time taken to reach the ground:

time taken to reach the ground = 2 * time taken to reach max height

(Since the dart will take the same time to come back down)

Time taken to reach the ground = 2 * 1.24

Time taken to reach the ground = 2.48 seconds

Therefore, the dart will hit the ground and stop 2.48 seconds after throwing

Explaining the concept:

From newton's second equation of motion

s = ut + 1/2 at²

Since we need the max vertical height, we need the vertical component of the values,

so this equation can be rewritten for vertical height as :

s(vertical) = u(vertical)* t + 1/2 * a(vertical) * t²

from the last section, we know that the dart reaches its maximum height at  t = 1.24 seconds

replacing the values in this equation:

s(vertical) = (12.2 * 1.24) + 1/2 * (-9.8) * (1.24)²

s(vertical) = 15.128 + (-7.5)

s(vertical) = 7.63 m

Therefore, the maximum height of the dart is 7.63 m

Explaining the concept:

The range of the dart is the horizontal distance covered by the dart

from the second section, we know that the dart travels horizontally with a constant velocity of 7.05 m/s

from the third section, we know that the total time taken by the dart to hit the ground is 2.48 seconds

Since the horizontal velocity of the dart is constant, we can say that it moved horizontally for 2.48 seconds at a constant velocity of 7.05 m/s

Solving for the range:

s = ut + 1/2 at²            From the second equation of motion

this equation can be rewritten for horizontal distance as:

s(horizontal) = u(horizontal)* t + 1/2 (a)(t)²

The dart is moving at a constant velocity, that means that its acceleration is 0

s(horizontal) = u(horizontal)* t + 1/2 (0)(t)²

s(horizontal) = u(horizontal)* t

replacing the variables

s(horizontal) = 7.05 * 2.48   [here, 2.48 is the time taken by the dart to reach the ground and stop]

s(horizontal) = 17.484 m

The horizontal distance covered by the dart is 17.484 m

Therefore, the range of the dart is 17.484 m

Answer:

time =  2.49 s

max height = 7.61 m

range = 17.57 m

See below for exact values.

Explanation:

Since we are given the angle at which the object is tossed, this object is in projectile motion.

We are given the initial velocity of the dart, and we can use the angle to solve for its horizontal and vertical components.

Horizontal component:

Vertical component:

In order to find the time that the dart stays in the air, we can use the constant acceleration equation that does not include displacement. This equation is:

Since we solve for time using the vertical motion of the projectile, we will use this equation in terms of the y-direction.

We don't know what the final velocity of the dart when it reaches the ground is, but we do know that its final velocity when it reaches its maximum height is 0 m/s.

Therefore, we can solve for half of the full time that it takes the object to reach the ground, and double this value at the end.

Let's set the downwards direction to be negative and the upwards direction to be positive.

Using our knowledge and previous calculations, we know that:

The acceleration of gravity is in the y-direction and facing downwards, so that's why it is -9.8 m/s².

Substitute these values into the constant acceleration equation.

Subtract 14.1 * sin(60) from both sides of the equation.

Divide both sides of the equation by -9.8 to solve for t.

Now, this is only the time for half of the object's trajectory. Double it to find the total time the dart is aloft:

The dart is in the air for a total of 2.49 seconds.

We can find the maximum height of the dart by using another constant acceleration equation.

Since we don't have the final velocity of the object, we can use this equation:

Subtract [tex]x_i[/tex] from both sides to get the change in position, or delta x.

In order to find the maximum height, we need to use this equation in terms of the y-direction.

Remember that time is the same regardless of the x- or y- direction.

Now, we can solve for the displacement in the y-direction by plugging in the values that we know.

Note that we are using half of the time t, since this is where the maximum height occurs.

Plug these known values into the constant acceleration equation:

The maximum height of the dart is 7.61 meters.

Finding the range of the object in projectile motion involves the same constant acceleration equation, but this time we are solving for the displacement in the horizontal direction (x-direction). Therefore:

We know the horizontal component of the initial velocity vector, which is what we will be using.

The acceleration, of an object in projectile motion, in the x-direction is always 0 m/s².

We will use the full time of the object since we want to find the entire horizontal distance that the object covers. We have:

Plug these values into the constant acceleration equation.

The range of the dart is 17.57 meters.

Answer:

Explanation:

range of projectile = u² sin2θ / g

u = 30 m /s

θ = 40°

range = 30² x sin 80 / 9.8

= 90.44 m

b )

maximum altitude H = u² sin²θ / 2 x g

= 30² sin²40 / 9.8

= 37.94 m .

Answer:

Question 3: Shortest Wavelenght

Question 4: Longes Wavelenghth

Explanation:

Answer:

Linear velocity is speed in a straight line (measured in m/s) whileangular velocity is the change in angle over time (measured in rad/s, which can be converted into degrees as well).

Explanation:

hope this helps :)

Answer:

The fraction of its volume inside liquid  is increased .

Explanation:

According to principle pf floatation , an object floats on the surface of water

when the weight of  liquid displaced by it becomes equal to weight of the object . weight of the liquid depends upon the density of the liquid .

In the second case , when the body is dipped into liquid of lesser density , in order to balance the weight of body , more volume of liquid will be displaced so that weight of displaced liquid becomes equal to object's weight . So the body floats with greater depth inside liquid . The fraction of its volume inside liquid  is increased .

Answer:

39975kgm/s due east

Explanation:

Given parameters:

Mass of the blimp  = 533kg

Velocity  = +75m/s due east

Unknown:

Momentum of the body  = ?

Solution:

The momentum of a body is the amount of motion it posses.

 Momentum is the product of mass and velocity;

  Momentum = mass x velocity

  Insert the parameters and solve;

    Momentum  = 533 x 75  = 39975kgm/s

The momentum of the body is 39975kgm/s due east

The momentum of a 533 kg blimp moving east at +75 m/s is 39,975kgm/s.

Momentum of a body can be calculated by multiplying the mass of the substance by its velocity. That is;

Momentum (p) = mass (m) × velocity (v)

According to this question, a 533 kg blimp is said to be moving east at +75 m/s. The momentum is calculated thus:

Momentum = 533 × 75

Momentum = 39,975kgm/s.

Therefore, momentum of a 533 kg blimp moving east at +75 m/s is 39,975kgm/s

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Answer:

85.14 m

__________________________________________________________

(y) denotes "in the vertical direction"

(x) denotes "in the horizontal direction"

We are given:

Initial Horizontal velocity of the Ball (u(x)) = 19.8 m/s

Initial height of the ball (s(y)) = 92 m

Initial Vertical velocity of the Ball (u(y)) =  0 m/s

Time taken to reach the ground:

taking downwards direction as positive

Since the horizontal velocity is not opposed by any force, it will be the same until the ball reaches the ground

The vertical velocity will be increasing at a rate of (10 m/s)/s until the ball hits the ground

ay = 10 m/s²

So, while calculating the time. we can just ignore the horizontal velocity

Solving for the time taken:

s(y) = u(y)t + 1/2a(y)t²                                   [second equation of motion]

92 = (0)(t) + 1/2(10)(t)²                               [replacing the variables]

92 = 5t²

t² = 92/5                                            [dividing both sides by 5]

t = √18.4                                            [taking the square root of both sides]

t = 4.3 seconds

So, it took the ball 4.3 seconds to reach the ground

Horizontal Distance travelled by the ball:

We know that the ball will reach the ground in 4.3 seconds

Since the horizontal velocity will not change, the ball will move with a constant velocity of 19.8 m/s in the horizontal direction

Horizontal distance travelled:

s(x) = u(x)t + 1/2a(x)t²                    [second equation of motion]

s(x) = (19.8)(4.3) + 1/2(0)(t)²          [replacing the variables]

s(x) = 85.14 m

Hence, the ball travels 85.14 m horizontally

Answer:

Rutherford's gold foil experiment showed that the atom is mostly empty space with a tiny, dense, positively-charged nucleus. Based on these results, Rutherford proposed the nuclear model of the atom.

In the early 1900s, scientists thought that an atom consisted of a positive substance with negative charges scattered throughout the substance, but Rutherford explains that the positive charge is present at the center while the negative charges are present around it in the form of clouds.

There are various models that tried to explain the atomic model, and one  of that  Rutherford model is one in which he explains the model using the gold foil, which he then bombarded with the alpha particles. some of the particles that came back, while some passed through it by making some angles, and from this he concluded that the positive charge remains in the center while the negative is displaced.

Hence, in the early 1900s, scientists thought that an atom consisted of a positive substance with negative charges scattered throughout the substance, but Rutherford explains that the positive charge is present at the center while the negative charges are present around it in the form of clouds.

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Answer:

IF the price of chocolate increases, THEN the amount of chocolate people buy decreases

Explanation:

In a scientific investigation, an observation is first made. Based on this observation, a scientific question is then asked. However, a HYPOTHESIS is given next to explain the question asked. A hyothesis is a testable explanation given to solve an observed problem or provide a possible answer to a question.

The hypothesis must be subject to testing via EXPERIMENTATION. A hypothesis usually goes in an IF, THEN format. In this case with the testable question: How does price affect the amount of chocolate people buy?

A hypothesis that can explain this question is: IF the price of chocolate increases, THEN the amount of chocolate people buy decreases.

Answer:

0.14

Explanation:

Flow rate is the volume flowing through a point at a particular time, in calcuing flow rate we have

Q= v*t

it in terms of Area, we have Q= A*v

Where A= area

v= velocity.

Solving the question , flow rate is constant then

A*v= constant

A(i) v(i)= A(f) v(f)

Where A(i)= initial area= 1.00cm^2

A(f)= final area= 0.400cm^2

V(i) and V(f) are the initial and final velocity respectively and the ratio of the two will gives us the factor

Substitute the values into the equation we have

1 V(i)= 4 V(f)

But we were told that the cross sectional area of 1.00cm^2 branches into 18 smaller arteries.

Then

1 V(i)=0.4 V(f)*(18)

1 V(i)=7.2V(f)

Then if we find the ratio of the velocity, we will get the factor.

V(f)/V(i)= 1/7.2

V(f)/V(i)=0.14

Hence, the factor of the average velocity of the blood reduced when it passes into these branches is 0.14

Answer:

[tex]2.79 \times 10^5 \ \text{kg}[/tex]

Explanation:

Newton's Law of Universal Gravitation:

Let's convert our given information to scientific notation:

Now using the gravitational force and the distance between centers of mass that are given, we can plug these into Newton's law:

Remove the units for better readability.

Divide both sides of the equation by the gravitational constant G.

Distribute the power of 2 inside the parentheses.

If we evaluate the left side of the equation, we get:

Multiply both sides of the equation by r.

In order to find the mass of one asteroid, we can use the fact that both asteroids have the same mass, therefore, we can rewrite [tex]m_1m_2[/tex] as [tex]m^2[/tex].

Square root both sides of the equation.

Since m is in units of kg, we can state that the mass of each asteroid is 2.79 * 10⁵ kg.

Answer:

c. √2T

Explanation:

The period of a simple pendulum is given by;

[tex]T = 2\pi \sqrt{\frac{L}{g} } \\\\\frac{T}{2\pi} = \sqrt{\frac{L}{g}} \\\\\frac{T^2}{4\pi^2} = \frac{L}{g}\\\\\frac{g}{4\pi^2} = \frac{L}{T^2}\\\\ \frac{L_1}{T_1^2}= \frac{L_2}{T_2^2}\\\\T_2^2 = \frac{L_2T_1^2}{L_1}\\\\L_2 = 2L_1\\\\ T_2^2 = \frac{2L_1T_1^2}{L_1}\\\\ T_2^2 =2T_1^2\\\\T_2 = \sqrt{2T_1^2}\\\\T_2 = T_1\sqrt{2}[/tex]

Thus, the the new period will be √2T

Answer:

A

For Yanni, the speed of the ball is 23 m/s, and for the quarterback, the speed of the ball is 15 m/s.

Explanation:

Right on edge 2021

The statement supported by this scenario is, for Yanni, the speed of the ball is 23 m/s, and for the quarterback, the speed of the ball is 15 m/s.

The relative speed of the ball is determined with respect to frame of reference.

Vr/b = va + vb

Vr/b = 8 + 15 = 23 m/s

Vr/b = va + vb

Vr/b = 0 + 15 = 15 m/s

Thus, the statement supported by this scenario is, for Yanni, the speed of the ball is 23 m/s, and for the quarterback, the speed of the ball is 15 m/s.

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Answer:

C. 39 m/s

Explanation:

First we need to calculate the total force required to move the train along the inclined plane. So, it is clear that the work done will be equal to the component of the weight that is parallel to the inclined plane, because there is no frictional force present:

Force = F = mg Sin θ

where,

m = mass of train = 3.3 x 10⁶ kg

g = 9.8 m/s²

θ = Angle of Inclination = 0.64°

Therefore,

F = (3.3 x 10⁶ kg)(9.8 m/s²)Sin 0.64°

F = 3.612 x 10⁵ N

Now, the formula for power is:

P = FV

V = P/F

where,

V = Velocity of Train = ?

P = Power of Engine = 14 MW = 1.4 x 10⁷ W

Therefore,

V = 1.4 x 10⁷ W/3.612 x 10⁵ N

V = 38.75 m/s

which is approximately equal to:

C. 39 m/s

The speed of train is 39 m/s. Hence, option (C) is correct.

Given data:

The mass of train is, [tex]m = 3.3 \times 10^{6} \;\rm kg[/tex].

The angle of inclination is, [tex]\theta = 0.64^ {\circ}[/tex].

The useful power output value is, [tex]P= 14 \;\rm MW = 14 \times 10^{6} \;\rm W[/tex].

The work done will be equal to the component of the weight that is parallel to the inclined plane, because there is no frictional force present. So, the total force required to move the train along the inclined plane is given as,

[tex]F = mg sin \theta\\\\F = 3.3 \times 10^{6} \times 9.8 \times sin0.64\\\\F = 361233.75 \;\rm N[/tex]

Now, use the formula of the power to obtain the value of speed as,

[tex]P = F \times v\\\\14 \times 10^{6} =361233.75 \times v\\\\v \approx 38.75 \;\rm m/s[/tex]

Thus, the speed of train is 39 m/s. Hence, option (C) is correct.

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Answer:

1620000J

Explanation:

Given parameters:

Resistance  = 24ohm

Current  = 5A

Time  = 45min

Unknown:

Work done = ?

Solution:

Electrical work done is given as the product of power with time;

  Electrical work done  = power x time

     Power  = I²R

 Electrical work done  = I²R x time

Convert the given time to seconds;

          1min  = 60s

          45 min  = 45 x 60  = 2700s

Now,

  Work done  = 5² x 24 x 2700 = 1620000J

Answer:

1000 cm³

Explanation:

The product of powers property is a rule that helps in simplifying the difficulties that comes with multiplying powers of numbers. It states that when multiplying two powers having the same base, we take one of the base, and then just add the exponents.

This is illustrated in the example.

S¹ * S². The product of powers asks us to pick one of the bases, S, and then add up the powers, thus

S¹ * S² = S^(¹+²)

S¹ * S² = S³

Now, using this in our question, volume of the cube is S³. Since we aren't given a length, I'm going to assume a length.

L = 10 cm. We all know that all sides are equal in a cube,

So, S = 10 cm.

S³ = volume of the cube

V = 10³

V = 1000 cm³

Now, to test the property of products, we say

S = 10, even though it doesn't show any visible exponent, we know that it's raised to the power of 1, and thus

S = 10¹

V = S * S * S

V = 10¹ * 10¹ * 10¹

V = 10^(¹+¹+¹)

V = 10³

V = 1000 cm³

Justified.......

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We are given:

Initial velocity (u) = 32 m/s

Acceleration (a) = 3 m/s²

Displacement (s) = 40 m

Final Velocity (v) = v m/s

Solving for the Final Velocity:

from the third equation of motion:

v² - u² = 2as

replacing the variables

v² - (32)² = 2(3)(40)

v² = 240 + 1024

v² = 1264

v = √1264

v = 35.5 m/s

Therefore, the velocity of the bike after travelling 40 m is 35.5 m/s

The  bike's velocity after covering 40 m distance is 35.55 m/s.

Explanation:

Given:

The initial velocity of the bike = 32 m/s

The rate of acceleration of the bike = 3 ms^2

Distance covered by the bike  = 40 m

To find:

The final velocity of the bike.

Solution:

The initial velocity of the bike = u = 32 m/s

The rate of acceleration of the bike = a = 3 ms^2

Distance covered by the bike = s = 40 m

The final velocity of the bike = v

Using the third equation of motion, which is written as :

[tex]v^2-u^2=2as\\v^2-(32m/s)^2=2\times 3m/s^2\times 40m\\v^2-1024 m^2/s^2=240 m^2/s^2\\v^2=240 m^2/s^2+1024 m^2/s^2\\v^2=1264 m^2/s^2\\v=35.55 m/s[/tex]

The  bike's velocity after covering 40 m distance is 35.55 m/s.

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Answer:

The initial and final states of the hydrogen atom were n=2 and n=6 respectively.

Explanation:

We must first obtain the energy of the photon;

E= hc/λ

where;

h= Plank's constant = 6.6 * 10^-34 JS

c= speed of light = 3* 10^8 m/s

λ = wavelength of light= 411 nm = 411* 10^-9 m

Substituting values;

E = 6.6 * 10^-34 * 3* 10^8 / 411* 10^-9

E = 4.8 * 10^-19 J or 3.0 eV

But ;

En = 13.6/n^2

So E = En final - En initial

3.0  = -13.6(1/n^2final - 1/n^2initial)

If we substitute n^2final = 6 and n^2 initial = 2 then the RHS becomes approximately equal to the LHS

Therefore the initial and final states of the hydrogen atom were n=2 and n=6 respectively.

Answer:

Vf = 3.67 [m/s]

Explanation:

To solve this problem we must use the following equation of kinematics.

[tex]v_{f} ^{2} =v_{i} ^{2} -(2*a*x)[/tex]

where:

Vf = final velocity [m/s]

Vi = initial velocity = 4.3 [m/s]

a = acceleration or desacceleration = 0.5 [m/s²]

x = distance = 5 [m]

Note: The negative sign in the above equation means that the velocity of the ball is decreasing (desacceleration).

Now replacing:

Vf² = (4.3)² - (2*0.5*5)

Vf² = 18.49 - 5

Vf² = 13.49

using the square root, we have.

Vf = 3.67 [m/s]

Answer: an element is a substance that cannot be broken down. it can’t be chemically decomposed into a different substance. elements are made up of just one atom

Explanation:

Answer: Parallel

Explanation: Parallel because you don’t want all the lights to go out because of one light.

The electrical wiring and safety devices applied have to be perfect for non complainable circuit system  in houses. One thing have to ensure that all the electrical components needs to follow the requirements set by national electrical code.

Circuits are way for the passage of electrical current which consists of electrical wires and devices such as bulbs, fan etc. The circuit system have to be properly designed so that no overload or short circuit can be occured.

Proper thermal insulations for cables and wires have to be chosen. Moreover, all the electrical components should follow the standard requirements set by local bodies or national electrical code.

Safety devices such as circuit breaker or switches like fuse of standard quality must be applied to protect the devices. Circuit breakers are more better than fuses because they don't need replacements.

Similarly, the selection of wires of cables have to careful and need to check the quality of plastic sheaths on them.

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Answer:

United States

Explanation: