. a body of mass m and negligible size starts from rest and slides down the surface of a frictionless solid sphere of radius r. (see below.) prove that the body leaves the sphere when

Answer:

Look below

Explanation:

Part A:

The initial angular velocity of the rotor can be found using the formula:

ω = v/r

where ω is the angular velocity, v is the linear velocity, and r is the radius of the cylinder. Since the rotor is rotating at 9000 rpm, we can convert this to radians per second:

ωi = (9000 rpm) x (2π/60 s) = 942.48 rad/s

The final angular velocity is zero. The frictional torque acting on the rotor is given by:

τ = Iα

where τ is the torque, I is the moment of inertia, and α is the angular acceleration. The moment of inertia for a solid cylinder is:

I = (1/2)mr^2

Substituting in the given values and solving for α, we get:

α = τ/I = (1.73 m⋅N) / [(1/2)(3.72 kg)(0.0760 m)^2] = 371.7 rad/s^2

The final angular velocity is zero, so we can use the formula:

ωf^2 = ωi^2 + 2αθ

where θ is the angle of rotation. Solving for θ, we get:

θ = (ωf^2 - ωi^2) / (2α) = (0 - (942.48 rad/s)^2) / (2 x 371.7 rad/s^2) = 6.76 revolutions

Therefore, the rotor will turn approximately 6.76 revolutions before coming to rest.

Part B:

The time it takes for the rotor to come to rest can be found using the formula:

ωf = ωi + αt

where ωf is the final angular velocity, ωi is the initial angular velocity, and α is the angular acceleration. Solving for t, we get:

t = (ωf - ωi) / α = (0 - 942.48 rad/s) / 371.7 rad/s^2 = 2.535 s

Therefore, it will take approximately 2.535 seconds for the rotor to come to rest.

The total distance covered by the subway train is 1796.5 m. The result is obtained by using the equations in uniformly accelerated straight motion.

A uniformly accelerated straight motion is a motion with acceleration or deceleration in a straight line. The equations apply in horizontal dimension are

v₁ = v₀ + at

v₁² = v₀² + 2ax

x = v₀t + ½ at²

Where

A subway train starts from rest at a station.

Find the total distance covered!

When it accelerates, the distance is

x₁ = v₀t + ½ a₁t₁²

x₁ = 0 + ½ (1.60)(14.0)²

x₁ = 0 + 0.8(196)

x₁ = 156.8 m

The final speed after 14 s is

v₁ = v₀ + at

v₁ = 0 + (1.6)(14.0)

v₁ = 22.4 m/s

The speed later will be constant for t₂ = 70.0 s.

When it moves with a constant speed (22.4 m/s), the distance is

x₂ = v₁t₂

x₂ = 22.4(70)

x₂ = 1568 m

When it slows down until it stops (v₂ = 0), the distance is

v₂² = v₁² - 2a₂x₃

0 = 22.4² - 2(3.5)x₃

22.4² = 2(3.5)x₃

501.76 = 7x₃

x₃ = 71.68 m

The total distance covered will be

x = x₁ + x₂ + x₃

x = 156.8 m + 1568 m + 71.68 m

x = 1796.48

x = 1796.5 m

Hence, the subway train traveled for a total distance of 1796.5 m.

Learn more about uniformly accelerated straight motion here:

https://brainly.com/question/30537831

#SPJ4

The required, apple is moving at a velocity of 7 m/s when it hits the ground.

The equation of motion is a mathematical expression that describes the relationship between the position, velocity, and acceleration of an object. It can be used to predict the motion of an object

The velocity of the apple just before it hits the ground can be calculated using the equation of motion for freely falling objects, which is:

v = √2gs

where v is the final velocity, g is the acceleration due to gravity (9.8 m/s²),

v = √2gs

Substitute the values in the above equation,
v = √[2 × 9.8 × 2.5]
v = 7 m/s

So the apple is moving at a velocity of 7 m/s when it hits the ground.

Learn more about the equation of motion here:
https://brainly.com/question/8898885
#SPJ1

a. The gauge pressure at this depth is 250 kPa.

b. The net force due to the water outside and the air inside the bell on a circular glass window 30.0 cm in diameter is 7.5 kN.

What do you mean by pressure?

Pressure is a measure of the force applied over a given area and is usually expressed in units such as pascals (Pa) or pounds per square inch (psi). It is a fundamental physical quantity found in all areas of physics, including fluid dynamics, thermodynamics, and mechanics.

a. The pressure at a certain depth in a body of water is given by the equation P = ρgh, where ρ is the density of water, g is the acceleration due to gravity, and h is the depth of the water. In this case, the gauge pressure at a depth of 150 m is equal to 250 kPa.

b. The net force on the glass window can be calculated by using the formula F = Pπr2, where P is the pressure, π is the mathematical constant, and r is the radius of the window. In this case, the net force on the window is 7.5 kN, which can be calculated as 7.5kN = 250kPa × (0.15m)2 × 3.14.

To know more about pressure,

https://brainly.com/question/28012687

#SPJ1

The spring constant of the spring is 200 N/m.

option C.

The spring constant of the spring is calculated  by applying the following formula as shown below;

.

Mathematically, the formula for energy stored in a spring is given as;

U = ¹/₂kx²

where;

k = ( 2U ) / ( x² )

k = ( 2 x 1 J ) / ( 0.1 m )²

k = 200 N/m

Learn more about spring constant here: https://brainly.com/question/1968517

#SPJ1

Answer:

Explanation:

jajs poza

The center of mass of a right-circular cone with a base radius r, height h, and a non-uniform mass density varies as the square of the distance from apex (tip of the cone) is:

ρ(x, y, z) = k * (√(x^2 + y^2 + z^2))^2

where k is a constant of proportionality.

To find the center of mass of a right-circular cone with a base radius "r" and height "h", and a non-uniform mass density that varies as the square of the distance from the apex, we need to use the following formula:

Let "m" be the total mass of the cone, then the center of mass can be found using the following formulas for the x, y, and z-coordinates:

x-coordinate:

x_cm = (1/m) * ∫∫∫_V x * ρ(x, y, z) * dV

y-coordinate:

y_cm = (1/m) * ∫∫∫_V y * ρ(x, y, z) * dV

z-coordinate:

z_cm = (1/m) * ∫∫∫_V z * ρ(x, y, z) * dV

where V is the volume of the cone, ρ(x, y, z) is the mass density function, and the integration is performed over the entire volume of the cone.

Since the mass density varies as the square of the distance from the apex, we have:

ρ(x, y, z) = k * (√(x^2 + y^2 + z^2))^2

where k is a constant of proportionality.

Substituting this into the above equations, we can find the center of mass of the cone.

The final result will depend on the specific values of r, h, and k, and the integration may be challenging to perform analytically. But numerical integration methods can be used to approximate the center of mass with good accuracy.

Learn more about Find Center of Mass Cone here:

https://brainly.com/question/15561647

#SPJ4

In the real world, humans do not have a flat slope for weight detection. However, some devices such as cameras, electric scales, and airplanes may display a flat slope for weight detection.

For instance, when detecting a change in weight with a hand-held device, humans would be less accurate than with a more sophisticated device such as an electric scale. Furthermore, when detecting a change of weight in an environment with multiple stimuli, such as a room filled with noise, humans may not be able to accurately detect the change at all.

Learn more about flat slope:

https://brainly.com/question/8138633

#SPJ4

Spring force P on the cable if the spring is compressed 0.025 m when the mechanism is in the position shown is 0.198 kN.

When the mechanism is in the position indicated, the force P on the cable is 0.198 kN if the spring is compressed 0.025 m in 40 kg

When a spring mechanism is adjusted by a length away from its balance length, it exerts a force on items fastened to its end that is continuously coordinated towards its harmonic position. F = - kx. The term "spring steady" refers to the proportional constant k. It is a percentage of the solidity of the spring. The following power is negative (moving towards the left) if x is positive (uprooting to the right), and vice versa. As a result, the spring force often works to restore mass to its harmonious position. The force P on the cable is therefore 0.198 kN. when, the mechanism is in the position shown.

Learn more about Spring Force here

https://brainly.com/question/29671992

#SPJ4

The magnitude of the resultant would be 40 N, the location of the resultant is 0 m.

Resultant is a term used to refer to the combined effect of two or more forces acting on an object. It is the vector sum of the individual forces acting on the object, and can be determined by adding the individual vectors of the forces together.

The magnitude of the resultant of the distributed load can be calculated by summing the forces at each point and then resolving them into components. The location of the resultant can then be determined by calculating the moment of the distributed load.

For example, if the load is distributed over a distance of 4 m and has a magnitude of 10 N/m,
the magnitude of the resultant would be 40 N.
This can be calculated by summing the forces at the start and end points (40 N = 10 N + 10 N + 10 N + 10 N).
The location of the resultant can then be determined by calculating the moment of the distributed load.
This is done by finding the sum of the moments at each point and then dividing by the total force (location = moment / force).
In this case, the moment at each point is 0 Nm, so the location of the resultant is 0 m.

To learn more about resultant
https://brainly.com/question/110151
#SPJ4

Complete Question is attached Below:

The device which is used to measure the over all current through the circuit is an ammeter. Option d is the symbol of ammeter.

An ammeter is a device used to measure electric current in amperes, either in direct current (DC) or alternating current (AC). Because only a tiny fraction of the current is sent via the meter mechanism at high levels and the majority is carried by a shunt in parallel with the meter, an ammeter can measure a wide range of current values.

An ammeter is represented by a circle with a capital A inside it in circuit diagrams. Accuracy and working principles of ammeters differ. With accuracy ranging from 0.1 to 2.0 percent, the movement ammeter monitors direct current flowing through a coil hanging between the poles of a magnet.

A moving coil revolving in the field created by a stationary coil is how the electrodynamic ammeter works. Therefore, option d is correct.

Find more on ammeter:

https://brainly.com/question/18404570

#SPJ1

The symbol used in diagram to represent the device is ammeter symbol that is circle with an A in it.

Electric current is defined as the rate of flow of electrons in a conductor. The SI Unit of electric current is the Ampere.

In given circuit,

A device is added to the electrical circuit to measure the total current in the circuit,

Ammeter is the device used to measure the current in a circuit. The ammeter is connected in series with the circuit, so that the current to be measured flows directly through the ammeter.

Ammeter symbol is a circle with an A in it.

Hence, ammeter's symbol will be used in diagram to represent the device.

Learn more about electric current here:

https://brainly.com/question/29766827

#SPJ1

In an equal circuit, all parts are associated across one another, subsequent in precisely two arrangements of electrically normal places.

The complete power in a series circuit is equivalent to the amount of power disseminated by the individual resistors.

The complete power disseminated will be equivalent to the amount of the power dispersed by every individual obstruction. Contingent upon the qualities that are known, blends of the power equation, also as Ohm's regulation, can be utilized to work out power disseminated (or some other obscure worth).

An equal circuit disseminates more power than a series circuit. For similar arrangements of resistors, the complete obstruction of the equal circuit is consistently lower than the all-out opposition in a series circuit.

To learn more about circuits here

https://brainly.com/question/2969220

#SPJ4

Answer:

The greatest height will be as follows:

h = (v²sin2θ)/2g

h = [(30m/s)² (2)] / (2 × 9.8 m/s²)

h = 225m

The corresponding horizontal distance will be as follows:

d = (v² sinθcosθ)/g

d = [(30m/s)² (2 × 1)] / 9.8 m/s²

d = 306m

The time of flight will be as follows:

t = (2v sinθ) / g

t = (2 × 30m/s × 2) / 9.8 m/s²

t = 12.24s

The given problem is a projectile motion problem in Physics. It can be solved using the formulas of kinematics considering the initial velocity of the particle and the angle of projection. Substituting the given values in their respective formulas will determine the time of flight, maximum height, and horizontal distance.

The subject matter of this question is based on the physics principle of projectile motion. To solve this problem, we can use some basic formulas of kinematics regarding time of flight, maximum height, and horizontal distance. The angle of projection here is given as \\tan^{-1}2\\ which equals approximately 63.4 degrees.

Firstly, the time of flight (T) can be found using the formula: T = 2u*sin(theta)/g, where 'u' is the initial velocity, 'theta' is the angle of projection, and 'g' is the acceleration due to gravity (approx. 9.81 m/s\^2 ).

Secondly, the greatest height (H) can be found using the formula: H = u^2*sin^2(theta)/2g.

Last but not least, the horizontal distance or the range (R) can be found using the formula: R = u^2*sin(2*theta)/g.

By substituting the given values in these formulas, we will be able to find the time of flight, the greatest height, and the horizontal distance.

https://brainly.com/question/20627626

#SPJ2

Answer:

see below

Explanation:

we have ,

We know,

Work = mgh

Work = 1.5kg * 10m/s² * 0.2m

Work= 3J

and we are done!

The acceleration of the cart is 43.12 m/s².

Time it takes the cart to travel from the starting point to the ending point is 3.8 sec.

Acceleration of the cylinder is a = g - (v²)/R.

Time it takes the cylinder to travel from the top of the ramp to the bottom is d = v_0t + 1/2at².

a.) The acceleration of the cart can be calculated using the formula g = 9.8 m/s², where g is the acceleration due to gravity. a = F/m = m × g = 4.40 kg × 9.8 m/s² = 43.12 m/s²

b.) The time it takes the cart to travel from the starting point to the ending point can be calculated using the kinematic equation:

d = v_0t + 1/2at²,

where d is the distance traveled, v_0 is the initial velocity (which is 0 for this case), a is the acceleration (determined in part a), and t is the time.

366 m - 53 m = 313 m

313 = 0t + 1/2(43.12)t² = 1/2(43.12)t²

313 = 21.56t²,  t² = 313 / 21.56

t² = 14.52, t = √14.52 = 3.8 sec.

c.) The acceleration of the cylinder can be calculated using the formula a = g - (v²)/R, where v is the linear velocity of the cylinder's center of mass and R is the radius of the cylinder.

d.) The time it takes the cylinder to travel from the top of the ramp to the bottom can be calculated using the kinematic equation:

d = v_0t + 1/2at²,

where d is the distance traveled, v_0 is the initial velocity (which is 0 for this case), a is the acceleration (determined in part c), and t is the time.

Learn more on acceleration here: https://brainly.com/question/14344386

#SPJ1

The potential at location B must be 452 V + 339 V = 791 V.

Potential is the capacity to become or develop into something, either tangible or intangible. It is an opportunity that, when acted on, can bring about a desired outcome. Potential exists both within individuals and within organizations, and can be realized through purposeful effort, ambition, and hard work.

When a particle is released from rest at location A with a potential of 452 V and arrives at location B with a velocity vB, the work done on the particle in moving it from location A to location B is equal to the difference in potentials between the two locations, or (791 V - 452 V) = 339 V.
This means that the potential at location B must be 452 V + 339 V = 791 V.

When the particle is released from rest from location C with a potential of 791 V and arrives at location B with twice the speed it had previously, or 2vB,
the work done on the particle in moving it from location C to location B is equal to the difference in potentials between the two locations, or (791 V - 791 V) = 0 V.
This means that the potential at location B must be 791 V + 0 V = 791 V, which is the same as the potential at location C.

To learn more about potential
https://brainly.com/question/24933254
#SPJ4

The particle cannot accelerate toward the speed of light if no acceleration is applied. The correct answer is e) none of these.

The particle encounters a force of 10 N in the opposite direction of the initial force, creating an unbalanced force. This means that the particle experiences an acceleration of 10 N in the opposite direction, decelerating from its initial velocity.

However, since the acceleration caused by the second force is equal to the acceleration caused by the first force, the particle does not come to a rapid halt, but rather its velocity gradually decreases until it comes to a stop. This means that the correct answer to the question is b) decelerates gradually to a halt.

In order for the particle to theoretically tend to the speed of light, it must experience a constant acceleration in any direction.

Since the two forces are in opposite directions and of equal magnitude, the resultant force is zero, meaning that the particle experiences no acceleration and therefore its speed remains the same.

Learn more about force:

https://brainly.com/question/26115859

#SPJ4

The velocity of the object is (2.0 s) = 0+∫ = −3.2 m/s − 5 m/s = −8.2 m/s

Velocity is a vector quantity that measures the rate of change of an object's position. It is the speed of an object in a given direction and is usually represented by a vector with both magnitude (the speed) and direction. Velocity is the rate at which an object's position changes over time, or the derivative of an object's position with respect to time.

The velocity of the object at time t = 2.0 s can be calculated using the equation for velocity, =0+∫.
We can calculate the velocity at t = 2.0 s by first calculating the integral of the acceleration equation.
∫ = −(10/)sin(+3/2)
Substituting in t = 2.0 s, we get
∫ = −(10/)sin(2+3/2) = −(10/)sin(5/2) = −5 m/s
We then substitute this value into the equation for velocity and substitute in the initial velocity of the object at t = 0 s, 0 = −3.2 m/s, to get:
(2.0 s) = 0+∫ = −3.2 m/s − 5 m/s = −8.2 m/s

To learn more about velocity
https://brainly.com/question/24445340
#SPJ4

The time taken for the man's speed to reach 40 m/s is 8.15 seconds.

What do you mean by speed?

Speed is the rate at which something moves or operates. It is usually measured in units such as miles per hour (mph) or kilometers per hour (kph). Speed is often used to describe the rate of change in a physical quantity, such as the speed of light. It can also be used to describe the rate of change in a process or activity, such as the speed at which a computer can process data.

So,

V = 50(1-e^-0.21t)

40 = 50(1-e^-0.21t)

e^-0.21t = (50-40)/50

-0.21t = ln((50-40)/50)

t = ln((50-40)/50)/-0.21

t ≈ 8.15 seconds

Therefore, the time taken is 8.15 seconds.

To know more about speed,

https://brainly.com/question/13943409

#SPJ1

The energy transfers and transformations involved in the falling of a rock off a cliff into seawater occur in the following order: potential energy, kinetic energy, and finally thermal energy.

The energy transfers and transformations involved in the falling of a rock off a cliff into seawater can be ranked as follows:

In summary, the energy transfers and transformations involved in the falling of a rock off a cliff into seawater occur in the following order: potential energy, kinetic energy, and finally thermal energy.

Learn more about energy here:

https://brainly.com/question/11399976

#SPJ4

The average angular speed in each direction of the rotating head is 9.42 rad/s.

The average linear speed in each direction of the bristles against the teeth is 5.09 cm/s.

The approximate speed of the bristles against the teeth when brushing by hand with an ordinary toothbrush is 1.26 cm/s.

Part A: The formula ω = Δθ/Δt can be used to determine the rotating head's average angular speed in each direction.

Where Δθ denotes the angular displacement, Δt denotes the rotational time, and ω denotes the angular speed.

In this instance,

Δt = 1/(7600/2) s/rotation, and Δθ= 70.0 degrees = 70.0 x (π/180) radians.

Thus, ω = (70.0 x (π/180)) / (1/(7600/2)) = 9.42 rad/s is the average angular speed in each direction.

Part B: The following equation can be used to determine the average linear speed of the bristles against the teeth:

v = rω

where r is the head's radius (0.55 cm), v is the linear speed, and ω is the angular speed.

The average linear speed is therefore v = 0.55 x 9.42 = 5.09 cm/s in each direction (rounded to two significant figures)

Part C: Although it is challenging to measure precisely, it is possible to estimate the speed of the bristles against the teeth when brushing by hand with a regular toothbrush. The average linear speed can be estimated using the formula v = rΔθ/Δt if we suppose that the bristles rotate through an average displacement of 45 degrees five times each second.

Where Δθ = 45 degrees, Δt = 1/5 s, and r = the radius of the bristles (estimated as 0.2 cm).

So, the average linear speed is approximately:

v = 0.2 x (45 x (π/180)) / (1/5) = 1.26 cm/s (rounded to two significant figures).

Read more about Angular Speed:

https://brainly.com/question/6860269

#SPJ4

The vapor pressure of Substance X at -98. C is 1.01 atm, rounded to 2 significant digits.

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase. It is an indication of a liquid's evaporation rate. It is directly related to the vapor's temperature, and increases with increasing temperature.

ln (P2/P1) = (ΔHvap/R) * ((1/T1) – (1/T2))
where:
P2 = vapor pressure of the substance at temperature T2
P1 = vapor pressure of the substance at temperature T1
ΔHvap = enthalpy of vaporization of the substance
R = ideal gas constant
T1 = normal boiling point of the substance
T2 = temperature at which the vapor pressure is being calculated
In this case, we are trying to calculate the vapor pressure of Substance X at -98. C.
We can plug in the known values into the equation to calculate the vapor pressure of Substance X at -98. C:
ln (P2/P1) = (21.0 kj/mol/8.314 J/mol-K) * ((1/19) – (1/273))
ln (P2/P1) = 0.0087
P2 = exp (0.0087) * P1
P2 = 1.009 * P1
P2 = 1.009 * 1.00 atm (atm is the vapor pressure of Substance X at 19. C, its normal boiling point)
P2 = 1.009 atm
Therefore, the vapor pressure of Substance X at -98. C is 1.01 atm, rounded to 2 significant digits.

To learn more about vapor pressure
https://brainly.com/question/2272852
#SPJ4

The electron gains more kinetic energy than the proton when accelerated through a potential difference of 1 V.

The relationship between the kinetic energies of the electron and proton can be determined using the formula for the kinetic energy of a particle:

[tex]KE = (1/2)mv^2[/tex]

[tex]V = (q/m)d[/tex]

where V is the potential difference, q is the charge, m is its mass, and d is the distance .

For the electron, [tex]V = 1 V[/tex]and[tex]q/m = -1.6 x 10^-19 C/kg[/tex], so its final velocity is:

[tex]v_e = sqrt((2qV)/m) = sqrt((2*(-1.6 x 10^-19)*1)/9.11 x 10^-31) = 5.93 x 10^6 m/s[/tex]

For the proton, [tex]V = -1 V and q/m = 1.6 x 10^-19 C/kg,[/tex] so its final velocity is:

[tex]v_p = sqrt((2qV)/m) = sqrt((2*(1.6 x 10^-19)*(-1))/1.67 x 10^-27) = 7.16 x 10^5 m/s[/tex]

Substituting these values into the formula for kinetic energy, we get:

[tex]KE_e = (1/2)9.11 x 10^-31(5.93 x 10^6)^2 = 1.63 x 10^-17 J[/tex][tex]KE_p = (1/2)1.67 x 10^-27(7.16 x 10^5)^2 = 0.84 x 10^-17 J[/tex]

Therefore, we have:

[tex]KE_e > KE_p[/tex] , This is because the electron has a much smaller mass than the proton, so it experiences a much larger acceleration and gains more velocity and kinetic energy.

To know more about  Potential difference, here

https://brainly.com/question/21808222

#SPJ4

(a) The centripetal acceleration of the ball at 7.72 rev/s is 30.2m/s²

(b) The centripetal acceleration at 6.39 rev/s is 33.9m/s².

What is a radius?

Using the definition of speed and noting that the ball travels in a circular path,

v= d/Δt

= 2πR/T

​where R is the radius of the circle and T is the period, that is, the time interval required for the ball to go around once. For the periods given in the problem,

8.00rev/s→T= 1/8.00rev/s =0.125s

6.00rev/s→T= 1/6.00rev/s =0.167s

Therefore, the speeds in the two cases are:  8.00rev/s→v= 2π(0.600m)/ 0.125s

​ =30.2m/s²

6.00rev/s→v= 2π(0.900m)/0.167s

=33.9m/s²

Therefore, 6.00rev/s gives the greater speed of the ball.

To know more about radius, click the link given below:

https://brainly.com/question/13449316

#SPJ4

At that point in its motion, the ball changes direction without changing its speed, is the a true statement.

Instantaneous acceleration refers to the rate of change of an object's velocity at a specific point in time. It measures the change in an object's velocity over an infinitesimal amount of time and is the derivative of velocity with respect to time.

This statement is true because when the acceleration vector is perpendicular to the velocity vector, it means the ball is changing direction without changing its speed. The direction of the acceleration vector determines the change in direction, and the magnitude of the acceleration vector determines the rate of change in speed. If the acceleration vector is perpendicular to the velocity vector, it means that the direction is changing, but the speed is not changing.

Learn more on instantaneous acceleration here: https://brainly.com/question/28293905

#SPJ1

Between the plates, there is a 14 x 10^6 V/m electric field. The plates have a charge density of 2.32 x 10-17 C/m^2 C. The net charge on the membrane piece is 0 C, and the charge on each side of the membrane is 3 x 10-8 C in magnitude.

Part A:

Part B:

Part C:

Read more about Electromagnetism:

https://brainly.com/question/24319848

#SPJ4

The spring constant of the spring is 5.1N/m.

The formula for calculating the period of oscillation is expressed as:

[tex]T = 2\pi \sqrt{\dfrac{m}{k}}[/tex]

,where m is the mass of the spring and k is the spring constant.

Making the spring constant "k" the subject of the formula will give;

[tex]k = 4\pi^2\dfrac{m}{T^2}[/tex]

Get the period of oscillation "T"

[tex]T = \dfrac{1}{f}[/tex]

frequency "f" is the number of oscillations completed in one second.

If a student with a stopwatch finds that 8 oscillations take 12.0 s, the number of oscillations in one sec will be 12/8 = 1.5 oscillations.

Period T = 1/1.5 = 0.67 seconds

Get the required spring constant,

   [tex]k = 4\pi^2\dfrac{0.240}{(0.67)^2}\\k = 21.06[/tex]

Hence the spring constant of the spring is 21.06 N/m.

To know more about the spring constant, here

https://brainly.com/question/14159361?referrer=searchResults

#SPJ4