Dr. Yehia Eissa
PHYS101
Sheet 6
Chapters 7 & 8: Work and Energy
1. A shopper in a supermarket pushes a cart with a force of 35.0 N directed at an angle of 25.0°
downward from the horizontal. Find the work done by the shopper on the cart as he moves down
an aisle 50.0 m long.
2. A force F = (6i - 2j) N acts on a particle that under-goes a displacement r = (3i + j) m. Find (a)
the work done by the force on the particle and (b) the angle between F and r.
3. The force acting on a particle is Fx = (8x - 16) N, where x is in meters. (a) Make a plot of this
force versus x from x = 0 to x = 3.00 m. (b) From your graph, find the net work done by this force
on the particle as it moves from x = 0 to x = 3.00 m.
4. A force F = (4xi + 3yj) N acts on an object as the object moves in the x direction from the origin
to x = 5.00 m. Find the work W= F. dr done on the object by the force.
5. If it takes 4.00 J of work to stretch a Hooke’s-law spring 10.0 cm from its unstressed length,
determine the extra work required to stretch it an additional 10.0 cm.
6. A 4.00-kg particle is subject to a total force that varies with position as shown in Figure P7.13.
The particle starts from rest at x= 0. What is its speed at (a) x = 5.00 m, (b) x = 10.0 m, (c) x =
15.0 m?
7. A 2.00-kg block is attached to a spring of force constant 500 N/m as in Figure 7.10. The block is
pulled 5.00 cm to the right of equilibrium and released from rest. Find the speed of the block as it
passes through equilibrium if (a) the horizontal surface is frictionless and (b) the coefficient of
friction between block and surface is 0.350.
8. The electric motor of a model train accelerates the train from rest to 0.620 m/s in 21.0 ms. The
total mass of the train is 875 g. Find the average power delivered to the train during the
acceleration.
9. A 200-g block is pressed against a spring of force constant 1.40 kN/m until the block compresses
the spring 10.0 cm. The spring rests at the bottom of a ramp inclined at 60.0° to the horizontal.
Using energy considerations, determine how far up the incline the block moves before it stops (a)
if there is no friction between the block and the ramp and (b) if the coefficient of kinetic friction is
0.400.
10. A 400-N child is in a swing that is attached to ropes 2.00 m long. Find the gravitational potential
energy of the child–Earth system relative to the child’s lowest position when (a) the ropes are
horizontal, (b) the ropes make a 30.0° angle with the vertical, and (c) the child is at the bottom of
the circular arc.
11. A block of mass 0.250 kg is placed on top of a light vertical spring of force constant 5 000 N/m
and pushed downward so that the spring is compressed by 0.100 m. After the block is released
from rest, it travels upward and then leaves the spring. To what maximum height above the point
of release does it rise?
12. Two objects are connected by a light string passing over a light frictionless pulley as shown in
Figure P8.13. The object of mass 5.00 kg is released from rest. Using the principle of conservation
of energy, (a) determine the speed of the 3.00-kg object just as the 5.00-kg object hits the ground.
(b) Find the maximum height to which the 3.00-kg object rises.
13. A particle of mass m = 5.00 kg is released from point A and slides on the frictionless track shown
in Figure P8.24. Determine (a) the particle’s speed at points B and C and (b) the net work done by
the gravitational force in moving the particle from A to C.
14. The coefficient of friction between the 3.00-kg block and the surface in Figure P8.31 is 0.400. The
system starts from rest. What is the speed of the 5.00-kg ball when it has fallen 1.50 m?
15. A 3.00-kg crate slides down a ramp. The ramp is 1.00m in length and inclined at an angle of
30.0°, as shown in Figure 8.11. The crate starts from rest at the top, experiences a constant friction
force of magnitude 5.00N, and continues to move a short distance on the horizontal floor after it
leaves the ramp. Use energy methods to determine the speed of the crate at the bottom of the
ramp.