chapter 6
A man carries a 12-kg chair up one flight of stairs to the second floor of his house. If the second floor is 3.3 m above the first floor, what is the change in the gravitational potential energy of the chair?
+390 J
What is the work done by the force of gravity when a 20.0-kg weight is displaced vertically upward a distance of 3.0 m?
-600 J
Consider the force F shown in the drawing. This force acts on an object that can move along the positive or negative x axis, or along the positive or negative y axis. The work done by this force is positive when the displacement of the object is along the __________ axis or along the __________ axis.
-x, +y
A stone sphere of radius 7.00 m rests in a flat field. Relative to the ground, what is the gravitational potential energy of a 90.0-kg person sitting on the very top of the sphere?
1.23 × 104 J
A 1500-kg elevator moves upward with constant speed through a vertical distance of 25 m. How much work was done by the tension in the elevator cable?
370 000 J
In which one of the following situations will there be an increase in kinetic energy?
A ball starts from rest and freely rolls downhill.
Which one of the following situations is an example of a conservative force acting?
A child jumping on a trampoline is pushed upward by an elastic spring force.
Alice and Bill, who happen to have the same mass, both want to climb to the top of a mountain. Bill wants to take the steep path straight up, but Alice wants to take the path that gently winds around the mountain, even though it is 8 times longer than the steep path. They both eventually reach the top of the mountain, but Alice reaches the top in 1/3 the time that Bill takes using the steep route. How does the work that Alice did in climbing the mountain compare with the amount that Bill did?
Alice and Bill did the same amount of work.
In which one or more of the following situations is the principle of conservation of mechanical energy obeyed?
An object moves uphill with a decreasing speed, An object moves downhill with an increasing speed.
A net external force acts on a particle that is moving along a straight line. This net force is not zero. Which one of the following statements is correct?
Both the velocity and the kinetic energy of the particle are changing.
The same force F pushes in three different ways on a box moving with a velocity v, as the drawings show. Rank the work done by the force F in ascending order (smallest first).
C, A, B
A glass slips off the table and falls to the floor, breaking into several pieces. Once the pieces come to rest, all of the glass's initial gravitational potential energy it had on the table is now lost.
False
A force does positive work on a particle that has a displacement pointing in the +x direction. This same force does negative work on a particle that has a displacement pointing in the +y direction. Toward which quadrant of the x, y coordinate system does the force point?
Fourth
In a simulation on earth, an astronaut in his space suit climbs up a vertical ladder. On the moon, the same astronaut makes the exact same climb. Which one of the following statements describes how the gravitational potential energy of the astronaut changes during the climb?
It changes by a greater amount on the earth.
The table lists the initial and final kinetic and potential energies for a number of different motions. Identify the one for which mechanical energy is not conserved by determining the work Wnc done by the net nonconservative force.
Motion D, Wnc = -465 J
A box is being moved with a velocity v→v→ by a force P→P→ (in the same direction as v→v→) along a level horizontal floor. The normal force is FN−→FN→, the kinetic frictional force is fk→fk→, and the weight is mg→mg→. Which one of the following statements is correct?
P→P→ does positive work, FN−→FN→ and mg→mg→ do zero work, and fk→fk→ does negative work.
Sara carries a heavy box of books down a flight of stairs from the third floor to the first floor. Which one of the following statements best describes the work done on the box by Sara?
Sara does a large amount of negative work on the heavy box of books.
Consider a skier sliding down a mountain slope with no friction. What can you say about the sign of the change in the skier's kinetic energy and the change in her gravitational potential energy?
The change in her kinetic energy is positive, and the change in her gravitational potential energy is negative.
A force F acts on an object undergoing a displacement s, the force being oriented at an angle θ with respect to the displacement. Which one of the following correctly describes ALL of the circumstances under which the work done by the force is zero?
The force is zero, or the displacement is zero, or the angle is 90°.
A nonzero net force acts on a particle and does work. Which one of the following statements is true?
The kinetic energy, speed, and velocity of the particle change.
Two balls of equal size are dropped from the same height from the roof of a building. One ball has twice the mass of the other. When the balls reach the ground, how do the kinetic energies of the two balls compare?
The lighter one has one half as much kinetic energy as the other does.
An elevator supported by a single cable descends a shaft at a constant speed. The only forces acting on the elevator are the tension in the cable and the gravitational force. Which one of the following statements is true?
The net work done by the two forces is zero joules.
Which one of the following statements concerning the principle of conservation of energy is false?
The net work done on an object must be zero joules since energy is neither created nor destroyed in the process.
A ball is constrained to follow a circular path by a conservative force. During a time interval t, the ball makes exactly one revolution. Which one of the following statements concerning the net work done on the ball during time t is true?
The net work is equal to zero joules.
In which one of the following circumstances does the principle of conservation of mechanical energy apply, even though a nonconservative force acts on the moving object?
The nonconservative force is perpendicular to the displacement of the object.
A net external nonconservative force does positive work on a particle. Based solely on this information, you are justified in reaching only one of the following conclusions. Which one is it?
The total mechanical energy of the particle increases.
Two forces F1 and F2 act on a particle. As a result the speed of the particle increases. Which one of the following is NOT possible?
The work done by each force is negative.
Which one of the following situations is an example of an object with a non-zero kinetic energy?
a satellite in geosynchronous orbit
An object is initially at height y1. After a time interval t, the object is located at height y2. The work done by the gravitational force on the object is dependent on which of the following quantities?
a) y1 - y2
Suppose the total mechanical energy of an object is conserved. Which one or more of the following statements is/are true?
all of the above
Complete the following statement: In situations involving non-conservative external forces, the work done by these forces
can be either positive or negative
Complete the following statement: The net work done by a conservative force acting on an object
depends only on the starting and ending points.
Air resistance is a nonconservative force. It always opposes the motion of an object. An airplane flies from New York to Atlanta and then returns to its point of departure. The net work done by air resistance during this round trip ___________.
is negative
A person is riding on a Ferris wheel. When the wheel makes one complete turn, the net work done on the person by the gravitational force ____________.
is zero
A ball is thrown vertically upward in the air. Which one of the following quantities is necessarily equal to zero at the highest point of the ball's trajectory?
kinetic energy
Which one of the following choices is an example of a non-conservative force?
kinetic frictional force
A ball has a speed of 15 m/s. Only one external force acts on the ball. After this force acts, the speed of the ball is 7 m/s. Has the force done positive, zero, or negative work on the ball?
negative
A sailboat is moving at a constant velocity. Is work being done by a net external force acting on the boat?
no
A suitcase is hanging straight down from your hand as you ride an escalator. Your hand exerts a force on the suitcase, and this force does work. This work is
positive when you ride up and negative when you ride down.
Which one of the following has the largest kinetic energy?
the earth moving in its orbit around the sun
Complete the following statement: If positive work is done on a moving object,
the velocity of the object may increase.
Complete the following statement: The total mechanical energy of a system remains unchanged if
there are no external forces acting on the system.
A stone is thrown with a speed v0 and returns to earth, as the drawing shows. Ignore friction and air resistance, and consider the initial and final locations of the stone. Which one of the following correctly describes the change ΔPE in the gravitational potential energy and the change ΔKE in the kinetic energy of the stone as it moves from its initial to its final location?
ΔPE = 0 J and ΔKE = 0 J
