Question 1

A mass is pressed against (but is not attached to) an ideal horizontal spring on a frictionless horizontal surface. After being released from rest, the mass acquires a maximum speed v and a maximum kinetic energy K. If instead the mass initially compresses the spring twice as far:

Accepted Answer

The maximum potential energy stored in a spring is directly proportional to the square of the displacement of the spring from its equilibrium position. Therefore, when the mass is compressed twice as far, the spring stores four times as much potential energy (since the displacement is squared). When the mass is released, this stored energy is converted into kinetic energy. Since the potential energy is doubled, the kinetic energy must also be doubled, so the correct choice is C. The maximum speed will not be affected by the amount of compression of the spring, so choices A, B, D, and E can be eliminated.

Question 2

An 8.0-m massless rod is loosely pinned to a frictionless pivot at 0, as shown in the figure. A very small 4.0-kg ball is attached to the other end of the rod. The ball is held at A, where the rod makes a 30° angle above the horizontal, and is released. The ball-rod assembly then swings freely with negligible friction in a vertical circle between A and B. The tension in the rod when the ball passes through the lowest point at D is closest to

Accepted Answer

The answer of An 8.0-m massless rod is loosely pinned...

Question 3

A block slides down a frictionless inclined ramp. If the ramp angle is 17.0° and its length is 30.0 m, find the speed of the block as it reaches the bottom of the ramp, assuming it started sliding from rest at the top.

Accepted Answer

The speed of the block can be found using energy conservation. The potential energy at the top is converted to kinetic energy at the bottom. Using the formula v = sqrt(2gh), where h = 30.0 * sin(17°), the speed v is approximately 13.1 m/s.

Question 4

In the figure, a 4.0-kg ball is on the end of a 1.6-m rope that is fixed at 0. The ball is held at point A, with the rope horizontal, and is given an initial downward velocity. The ball moves through three quarters of a circle with no friction and arrives at B, with the rope barely under tension. The initial velocity of the ball, at point A, is closest to

Accepted Answer

The answer of In the figure, a 4.0-kg ball is...

Question 5

A car on a roller coaster starts at zero speed at an elevation above the ground of 26 m. It coasts down a slope, and then climbs a hill. The top of the hill is at an elevation of 16 m. What is the speed of the car at the top of the hill? Neglect any frictional effects.

Accepted Answer

To solve this problem, we can use conservation of energy. At the top of the roller coaster, all of the energy is in the form of potential energy:

mgh = (1/2)mv^2

where m is the mass of the car, g is the acceleration due to gravity, h is the height above ground, and v is the speed of the car.

We can solve for v by plugging in values:

mgh = (1/2)mv^2 
mg(h - 16) = (1/2)mv^2  (using the height of the hill as the reference level)
2gh - 32g = v^2 
v = sqrt(2gh - 32g) = sqrt(2*9.81*10) = 14 m/s

So the answer is A) 14 m/s.

Question 6

In the figure, a stunt car driver negotiates the frictionless track shown in such a way that the car is barely in contact with the track at the top of the loop. The radius of the track is 9.9 m and the mass of the car is 1800 kg. Find the magnitude of the force of the car on the track when the car is at point A. You can treat the car as a point mass.

Accepted Answer

The answer of In the figure, a stunt car driver...

Question 7

A very small 100-g object is attached to one end of a massless 10-cm rod that is pivoted without friction about the opposite end. The rod is held vertical, with the object at the top, and released, allowing the rod to swing. What is the speed of the object at the instant that the rod is horizontal?

Accepted Answer

The potential energy at the top is converted to kinetic energy at the horizontal position. Using conservation of energy: mgh = 0.5mv^2, where h = 0.1 m. Solving gives v = sqrt(2gh) = sqrt(2*9.8*0.1) = 1.4 m/s.

Question 8

In the figure, a 5.00-kg block is moving at 5.00 m/s along a horizontal frictionless surface toward an ideal massless spring that is attached to a wall. After the block collides with the spring, the spring is compressed a maximum distance of 0.68 m. What is the speed of the block when it has moved so that the spring is compressed to only one-half of the maximum distance?

Accepted Answer

The answer of In the figure, a 5.00-kg block is...

Question 9

A 2.0 g bead slides along a frictionless wire, as shown in the figure. At point A, the bead is moving to the right but with negligible speed.  
(a) What is the potential energy of the bead at point A?
(b) What is the kinetic energy of the bead at point B?
(c) What is the speed of the bead at point B?
(d) What is the speed of the bead at point C?

Accepted Answer

The answer of A 2.0 g bead slides along a...

Question 10

A 60.0-kg person drops from rest a distance of 1.20 m to a platform of negligible mass supported by an ideal stiff spring of negligible mass. The platform drops 6.00 cm before the person comes to rest. What is the spring constant of the spring?

Accepted Answer

The answer of A 60.0-kg person drops from rest a...

Question 11

A roller coaster of mass 80.0 kg is moving with a speed of 20.0 m/s at position A as shown in the figure. The vertical height above ground level at position A is 200 m. Neglect friction.  
(a) What is the total mechanical energy of the roller coaster at point A?
(b) What is the total mechanical energy of the roller coaster at point B?
(c) What is the speed of the roller coaster at point B?
(d) What is the speed of the roller coaster at point C?

Accepted Answer

The answer of A roller coaster of mass 80.0 kg...

Question 12

A 50.0-kg skier starting from rest travels 200 m down a hill that has a 20.0° slope and a uniform surface. When the skier reaches the bottom of the hill, her speed is 30.0 m/s.
(a) How much work is done by friction as the skier comes down the hill?
(b) What is the magnitude of the friction force if the skier travels directly down the hill?

Accepted Answer

The answer of A 50.0-kg skier starting from rest travels...

Question 13

A spring-loaded dart gun is used to shoot a dart straight up into the air, and the dart reaches a maximum height of 24 meters above its point of release. The same dart is shot up a second time from the same gun, but this time the spring is compressed only half as far (compared to the first shot). How far up does the dart go this time? (Neglect friction and assume the spring is ideal and massless.)

Accepted Answer

The distance the dart travels is directly proportional to the square of the spring compression. Halving the compression distance results in a quarter (1/4) of the original height, so 24 meters divided by 4 equals 6 meters.

Question 14

A small hockey puck slides without friction over the icy hill shown in the figure and lands 6.20 m from the foot of the cliff with no air resistance. What was its speed v0 at the bottom of the hill?

Accepted Answer

The answer of A small hockey puck slides without friction...

Question 15

A 2.0-kg object is moving without friction along the x-axis. The potential energy curve as a function of position is shown in the figure, and the system is conservative. If the speed of the object at the origin is 4.0 m/s, what will be its speed at 7.0 m along the +x-axis?

Accepted Answer

The answer of A 2.0-kg object is moving without friction...

Question 16

A projectile is fired from ground level at an angle of 40.0° above horizontal at a speed of 30.0 m/s. What is the speed of the projectile when it has reached a height equal to 50.0% of its maximum height?

Accepted Answer

The speed of the projectile is given by:$$v = v_0\sqrt{\frac{2h}{h_{max}}}$$where:* v is the speed of the projectile at height h* v0 is the initial speed of the projectile* h is the height of the projectile* hmax is the maximum height of the projectileWe are given that h = 50.0% of hmax, so:$$h = 0.500h_{max}$$Substituting this into the equation for v, we get:$$v = v_0\sqrt{\frac{2(0.500h_{max})}{h_{max}}}$$$$v = v_0\sqrt{1.00}$$$$v = v_0$$Therefore, the speed of the projectile when it has reached a height equal to 50.0% of its maximum height is equal to its initial speed, which is 30.0 m/s.

Question 17

A 2.0 kg mass is moving along the x-axis. The potential energy curve as a function of position is shown in the figure. The kinetic energy of the object at the origin is 12 J. The system is conservative, and there is no friction.  
(a) What will be the kinetic energy at 2.0 m along the +x-axis?
(b) What will be the speed of the object at 6.0 m along the +x-axis?

Accepted Answer

The answer of A 2.0 kg mass is moving along...

Question 18

An object is attached to a hanging unstretched ideal and massless spring and slowly lowered to its equilibrium position, a distance of 6.4 cm below the starting point. If instead of having been lowered slowly the object was dropped from rest, how far then would it then stretch the spring at maximum elongation?

Accepted Answer

The answer of An object is attached to a hanging...

Question 19

In the figure, a very small toy race car of mass m is released from rest on the loop-the-loop track. If it is released at a height 2R above the floor, how high is it above the floor when it leaves the track, neglecting friction?

Accepted Answer

The answer of In the figure, a very small toy...

Question 20

Consider the motion of a 1.00-kg particle that moves with potential energy given by U(x) = (-2.00 J∙m)/x + (4.00 J∙m²)/x². Suppose the particle is moving with a speed of 3.00 m/s when it is located at x = 1.00 m. What is the speed of the object when it is located at x = 5.00 m?

Accepted Answer

First, we can use conservation of energy to find the total energy of the particle at x=1.00 m:
E = K + U = (1/2)mv^2 - (2.00 J*m)/x + (4.00 J*m/(x^12)) = 1.5 J
Then, we can use conservation of energy again to find the speed at x=5.00 m:
E = (1/2)mv^2 - (2.00 J*m)/x + (4.00 J*m/(x^12)) = 1.5 J
(1/2)(1.00 kg)v^2 - (2.00 J*m)/5.00 m + (4.00 J*m/(5.00 m)^2) = 1.5 J
Solving for v, we get v = 3.67 m/s, which is choice D.

Quiz 7: Potential Energy and Energy Conservation

A mass is pressed against (but is not attached to) an ideal horizontal spring on a frictionless horizontal surface. After being released from rest, the mass acquires a maximum speed v and a maximum kinetic energy K. If instead the mass initially compresses the spring twice as far:

A block slides down a frictionless inclined ramp. If the ramp angle is 17.0° and its length is 30.0 m, find the speed of the block as it reaches the bottom of the ramp, assuming it started sliding from rest at the top.

A car on a roller coaster starts at zero speed at an elevation above the ground of 26 m. It coasts down a slope, and then climbs a hill. The top of the hill is at an elevation of 16 m. What is the speed of the car at the top of the hill? Neglect any frictional effects.

A very small 100-g object is attached to one end of a massless 10-cm rod that is pivoted without friction about the opposite end. The rod is held vertical, with the object at the top, and released, allowing the rod to swing. What is the speed of the object at the instant that the rod is horizontal?

A 60.0-kg person drops from rest a distance of 1.20 m to a platform of negligible mass supported by an ideal stiff spring of negligible mass. The platform drops 6.00 cm before the person comes to rest. What is the spring constant of the spring?

A small hockey puck slides without friction over the icy hill shown in the figure and lands 6.20 m from the foot of the cliff with no air resistance. What was its speed v0 at the bottom of the hill?

A 2.0-kg object is moving without friction along the x-axis. The potential energy curve as a function of position is shown in the figure, and the system is conservative. If the speed of the object at the origin is 4.0 m/s, what will be its speed at 7.0 m along the +x-axis?

A projectile is fired from ground level at an angle of 40.0° above horizontal at a speed of 30.0 m/s. What is the speed of the projectile when it has reached a height equal to 50.0% of its maximum height?

In the figure, a very small toy race car of mass m is released from rest on the loop-the-loop track. If it is released at a height 2R above the floor, how high is it above the floor when it leaves the track, neglecting friction?

Consider the motion of a 1.00-kg particle that moves with potential energy given by U(x) = (-2.00 J∙m) /x + (4.00 J∙m²) /x². Suppose the particle is moving with a speed of 3.00 m/s when it is located at x = 1.00 m. What is the speed of the object when it is located at x = 5.00 m?

Quiz 7: Potential Energy and Energy Conservation

A mass is pressed against (but is not attached to) an ideal horizontal spring on a frictionless horizontal surface. After being released from rest, the mass acquires a maximum speed v and a maximum kinetic energy K. If instead the mass initially compresses the spring twice as far:

A block slides down a frictionless inclined ramp. If the ramp angle is 17.0° and its length is 30.0 m, find the speed of the block as it reaches the bottom of the ramp, assuming it started sliding from rest at the top.

A car on a roller coaster starts at zero speed at an elevation above the ground of 26 m. It coasts down a slope, and then climbs a hill. The top of the hill is at an elevation of 16 m. What is the speed of the car at the top of the hill? Neglect any frictional effects.

A very small 100-g object is attached to one end of a massless 10-cm rod that is pivoted without friction about the opposite end. The rod is held vertical, with the object at the top, and released, allowing the rod to swing. What is the speed of the object at the instant that the rod is horizontal?

A 60.0-kg person drops from rest a distance of 1.20 m to a platform of negligible mass supported by an ideal stiff spring of negligible mass. The platform drops 6.00 cm before the person comes to rest. What is the spring constant of the spring?

A small hockey puck slides without friction over the icy hill shown in the figure and lands 6.20 m from the foot of the cliff with no air resistance. What was its speed v0 at the bottom of the hill?

A 2.0-kg object is moving without friction along the x-axis. The potential energy curve as a function of position is shown in the figure, and the system is conservative. If the speed of the object at the origin is 4.0 m/s, what will be its speed at 7.0 m along the +x-axis?

A projectile is fired from ground level at an angle of 40.0° above horizontal at a speed of 30.0 m/s. What is the speed of the projectile when it has reached a height equal to 50.0% of its maximum height?

In the figure, a very small toy race car of mass m is released from rest on the loop-the-loop track. If it is released at a height 2R above the floor, how high is it above the floor when it leaves the track, neglecting friction?

Consider the motion of a 1.00-kg particle that moves with potential energy given by U(x) = (-2.00 J∙m) /x + (4.00 J∙m2) /x2. Suppose the particle is moving with a speed of 3.00 m/s when it is located at x = 1.00 m. What is the speed of the object when it is located at x = 5.00 m?

Consider the motion of a 1.00-kg particle that moves with potential energy given by U(x) = (-2.00 J∙m) /x + (4.00 J∙m²) /x². Suppose the particle is moving with a speed of 3.00 m/s when it is located at x = 1.00 m. What is the speed of the object when it is located at x = 5.00 m?