## Physics for Scientists

Physics & Astronomy

## Quiz 10 :

Interactions and Potential Energy

Looking for Introduction to Physical Science Homework Help?

Q02 Q02 Q02

Swimmers at a water park have a choice of two frictionless water slides as shown in the figure. Although both slides drop over the same height, h, slide 1 is straight while slide 2 is curved, dropping quickly at first and then leveling out. How does the speed v

_{1}of a swimmer reaching the end of slide 1 compares with v_{2}, the speed of a swimmer reaching the end of slide 2?Free

Unlocked

Multiple Choice

C

Q05 Q05 Q05

A box of mass m is pressed against (but is not attached to) an ideal spring of force constant k and negligible mass, compressing the spring a distance x. After it is released, the box slides up a frictionless incline as shown in the figure and eventually stops. If we repeat this experiment with a box of mass 2m

Free

Unlocked

Multiple Choice

Q06 Q06 Q06

A box of mass m is pressed against (but is not attached to) an ideal spring of force constant k and negligible mass, compressing the spring a distance x. After it is released, the box slides up a frictionless incline as shown in the figure and eventually stops. If we repeat this experiment but instead compress the spring a distance of 2x

Free

Unlocked

Multiple Choice

Q07 Q07 Q07

A box of mass m is pressed against (but is not attached to) an ideal spring of force constant k and negligible mass, compressing the spring a distance x. After it is released, the box slides up a frictionless incline as shown in the figure and eventually stops. If we repeat this experiment but instead use a spring having force constant 2k

Free

Unlocked

Multiple Choice

Q11 Q11 Q11

Block 1 and block 2 have the same mass, m, and are released from the top of two inclined planes of the same height making 30° and 60° angles with the horizontal direction, respectively. If the coefficient of friction is the same in both cases, which of the blocks is going faster when it reaches the bottom of its respective incline?

Free

Unlocked

Multiple Choice

Q12 Q12 Q12

A girl throws a stone from a bridge. Consider the following ways she might throw the stone. The speed of the stone as it leaves her hand is the same in each case, and air resistance is negligible. Case A: Thrown straight up.
Case B: Thrown straight down.
Case C: Thrown out at an angle of 45° above horizontal.
Case D: Thrown straight out horizontally.
In which case will the speed of the stone be greatest when it hits the water below?

Free

Unlocked

Multiple Choice

Q14 Q14 Q14

A potential energy function for system 1 is given by U

_{1}(x) = Cx^{2}+ Bx^{3}. The potential energy function for system 2 is given by U_{2}(x) = A + Cx^{2}+ Bx^{3}, where A is a positive quantity. How does the force on system 1 relate to the force on system 2 at a given position?Free

Unlocked

Multiple Choice

Q16 Q16 Q16

An 8.0-kg block is released from rest, with v

_{1}= 0.00 m/s, on a rough incline, as shown in the figure. The block moves a distance of 1.6-m down the incline, in a time interval of 0.80 s, and acquires a velocity of v_{2}= 4.0 m/s. How much work does gravity do on the block during this process?Free

Unlocked

Multiple Choice

Q17 Q17 Q17

You do 174 J of work while pulling your sister back on a swing, whose chain is 5.10 m long. You start with the swing hanging vertically and pull it until the chain makes an angle of 32.0° with the vertical with your sister is at rest. What is your sister's mass, assuming negligible friction?

Free

Unlocked

Multiple Choice

Q21 Q21 Q21

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?

Free

Unlocked

Essay

Q22 Q22 Q22

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?

Free

Unlocked

Essay

Q23 Q23 Q23

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:

Free

Unlocked

Multiple Choice

Q24 Q24 Q24

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?

Free

Unlocked

Short Answer

Q25 Q25 Q25

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

Free

Unlocked

Multiple Choice

Q26 Q26 Q26

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

Free

Unlocked

Multiple Choice

Q28 Q28 Q28

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?

Free

Unlocked

Short Answer

Q30 Q30 Q30

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.)

Free

Unlocked

Multiple Choice

Q32 Q32 Q32

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 ∙ m

^{2})/x^{2}. 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 ?Free

Unlocked

Multiple Choice

Q33 Q33 Q33

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.

Free

Unlocked

Multiple Choice

Q35 Q35 Q35

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?

Free

Unlocked

Multiple Choice

Q36 Q36 Q36

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?

Free

Unlocked

Multiple Choice

Q38 Q38 Q38

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?

Free

Unlocked

Multiple Choice

Q39 Q39 Q39

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.

Free

Unlocked

Short Answer

Q40 Q40 Q40

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?

Free

Unlocked

Essay

Q41 Q41 Q41

A 5.00-kg object moves clockwise around a 50.0 cm radius circular path. At one location, the speed of the object is 4.00 m/s. When the object next returns to this same location, the speed is 3.00 m/s.
(a) How much work was done by nonconservative (dissipative) forces as the object moved once around the circle?
(b) If the magnitude of the above nonconservative (dissipative) forces acting on the object is constant, what is the value of this magnitude?

Free

Unlocked

Short Answer

Q42 Q42 Q42

In the figure, a block of mass m is moving along the horizontal frictionless surface with a speed of 5.70 m/s. If the slope is 11.0° and the coefficient of kinetic friction between the block and the incline is 0.260, how far does the block travel up the incline?

Free

Unlocked

Short Answer

Q43 Q43 Q43

An object of mass 4.0 kg starts at rest from the top of a rough inclined plane of height 10 m as shown in the figure. If the speed of the object at the bottom of the inclined plane is 10 m/s, how much work does friction do on this object as it slides down the incline?

Free

Unlocked

Short Answer

Q44 Q44 Q44

An 0.80-kg block is held in place against the spring by a 67-N horizontal external force (see the figure). The external force is removed, and the block is projected with a velocity v

_{1}= 1.2 m/s upon separation from the spring. The block descends a ramp and has a velocity v_{2}= 1.9 m/s at the bottom. The track is frictionless between points A and B. The block enters a rough section at B, extending to E. The coefficient of kinetic friction over this section is 0.39. The velocity of the block is v_{3}= 1.4 m/s at C. The block moves on to D, where it stops. The spring constant of the spring is closest toFree

Unlocked

Multiple Choice

Q45 Q45 Q45

A 1.37-kg block is held in place against the spring by a 74-N horizontal external force (see the figure). The external force is removed, and the block is projected with a velocity v

_{1}= 1.2 m/s upon separation from the spring. The block descends a ramp and has a velocity at the bottom. The track is frictionless between points A and B. The block enters a rough section at B, extending to E. The coefficient of kinetic friction over this section is 0.24. The velocity of the block is at C. The block moves on to D, where it stops. The initial compression of the spring is closest toFree

Unlocked

Multiple Choice

Q46 Q46 Q46

A 1.86-kg block is held in place against the spring by a 81-N horizontal external force (see the figure). The external force is removed, and the block is projected with a velocity v

_{1}= 1.2 m/s upon separation from the spring. The block descends a ramp and has a velocity at the bottom. The track is frictionless between points A and B. The block enters a rough section at B, extending to E. The coefficient of kinetic friction over this section is 0.28. The velocity of the block is v_{3}= 1.4 m/s at C. The block moves on to D, where it stops. The height h of the ramp is closest toFree

Unlocked

Multiple Choice

Q47 Q47 Q47

A 2.5-kg box, sliding on a rough horizontal surface, has a speed of 1.2 m/s when it makes contact with a spring (see the figure). The block comes to a momentary halt when the compression of the spring is 5.0 cm. The work done by the friction, from the instant the block makes contact with the spring until is comes to a momentary halt, is -0.50 J. (a) What is the spring constant of the spring?
(b) What is the coefficient of kinetic friction between the box and the rough surface?

Free

Unlocked

Short Answer

Q48 Q48 Q48

The only force acting on an object moving along the x-axis is the conservative force given by F(x) = (2.00 N/m)x + (1.00 N/m

^{3})x^{3}. (a) What is the change in potential energy when the object moves from x = 1.00 m to x = 2.00 m? (b) What is the change in kinetic energy when the object moves from x = 1.00 m to x = 2.00 m?Free

Unlocked

Short Answer

Q55 Q55 Q55

When a particle is a distance r from the origin, its potential energy function is given by the equation U(r) = kr, where k is a constant and r = (a) What are the SI units of k?
(b) Find a mathematical expression in terms of x, y, and z for the y component of the force on the particle.
(c) If U = 3.00 J when the particle is 2.00 m from the origin, find the numerical value of the y component of the force on this particle when it is at the point (-1.00 m, 2.00 m, 3.00 m).

Free

Unlocked

Essay