Physics
Work
1) Three identical balls are thrown from the top of a building, all with the same initial
speed. The first is thrown horizontally, the second at some angle above the
horizontal, and the third at some angle below the horizontal, as shown in Figure 8.5.
Neglecting air resistance, rank the speeds of the balls at the instant each hits the
ground
2) A pendulum consists of a sphere of mass m attached to a light cord of length L, as shown in Figure
8.7. The sphere is released from rest when the cord makes an angle ϴA with the vertical, and
the pivot at P is frictionless. (a) Find the speed of the sphere when it is at the lowest point
B.
3) A 3.00-kg crate slides down a ramp. The ramp is 1.00 m in length and inclined at an angle of 30.0°,
as shown in Figure 8.8. The crate starts from rest at the top, experiences a constant frictional force of
magnitude 5.00 N, and continues to move a short distance on the flat
floor after it leaves the ramp. Use energy methods to determine the
speed of the crate at the bottom of the ramp.
4) A skier starts from rest at the top of a
frictionless incline of height 20.0 m, as shown in
Figure 8.10. At the bottom of the incline, she
encounters a horizontal surface where the
coefficient of kinetic friction between the skis and
the snow is 0.210. How far does she travel on
the horizontal surface before coming to rest?
5) A 4.00-kg particle moves from the origin to position C, which has
coordinates x =5.00 m and y =5.00 m (Fig. P8.3). One force on it is the
force of gravity acting in the negative y direction. Calculate the work
done by gravity as the particle moves from O to C along (a) OAC, (b)
OBC, and (c) OC. Your results should all be identical. Why?
Harshana Perera(B.Sc,BIT,SCJP)
2014 R kit
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Physics
Work
7) A particle of mass 0.500 kg is shot from P as shown in Figure P8.10. The particle has an initial
velocity vi with a horizontal component of 30.0 m/s. The particle rises
to a maximum height of 20.0 m above P. Using the law of conservation
of energy, determine (a) the vertical component of vi , (b) the work
done by the gravitational force on the particle during its motion from P
to B, and (c) the horizontal and the vertical components of the velocity
vector when the particle reaches B.
8) A particle of mass m =5.00 kg is released from point A and slides on the frictionless track shown in
Figure P8.13. Determine (a) the particle’s speed at points B and and (b) the net work done by the
force of gravity in moving the particle from A to B.
9) A particle of mass 8 kg is pulled at constant speed a distance of 28m up a rough plane which is
inclined at 30° to the horizontal. The coefficient of friction between the particle and the surface is 0.2.
Assuming the particle moves up a line of greatest slope, find:
(a) the work done against friction.
(b) the work done against gravity
10) A surface is inclined at an angle to the horizontal. A body of mass 78kg lies on the surface and is
pulled at a uniform speed a distance of 7.5m up a line of greatest slope against resistances totaling
60N. Find:
1) the work done against gravity.
2) the work done against the resistances
Harshana Perera(B.Sc,BIT,SCJP)
2014 R kit
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Physics
Work
 12 
co s 1  
 13  to the horizontal. A body of mass 140kg lies on
11) A rough surface is inclined at an angle
the surface and is pulled at a uniform speed a distance of 45m up the surface by a force acting along
the line of greatest slope. The coefficient of friction between the body and the surface is
2
 
7
Find:
1) the frictional force acting.
2) the work done against friction.
3) the work done against gravity
12) A rough surface is inclined at an angle co s 1  3  to the horizontal. A body of mass 90kg lies on the surface


 2 
and is pulled at a uniform speed a distance of 15m up the surface by a force acting along a line of greatest slope.
The coefficient of friction between the body and the surface is
a)
b)
1
 
8
Find:
the work done against friction.
the work done against gravity.
13) A van of mass 1600 kg starts from rest at a set of traffic lights. After travelling 240 m its speed is
23ms 1 . Given that the car is subject to a constant resistance of 450 N find the constant driving
force
14) A ball of mass 1.5kg is projected up a rough plane inclined at an angle of 30º to the horizontal with
a speed of 4 ms-1. Given that the coefficient of friction between the particle and the plane is 0.2 find
the distance the particle moves up the plane before coming to rest
A car of mass 1500kg is travelling along a level road against a constant resistance of magnitude 425
N. The engine of the car is working at 6 kW. Calculate:
(a) the acceleration when the car is travelling at 3ms
(b) the maximum speed of the car
1
15) A cyclist and bike have a combined mass of 85kg. If the cyclist is working at a constant rate of
250W against resistances totaling 18N calculate the maximum speed. The cyclist then ascends a
slope of incline 10º. If the cyclist continues to work at the same rate and the resistances remain
unchanged calculate the maximum speed up the incline
16) Bob is busy removing roof tiles from a house. He sends the tiles down a chute of length 12m,
inclined at an angle of 30º to the horizontal. The roof tiles weigh 4.5kg each and are released from
rest at the top of the chute. When the tile reaches the bottom it has a speed of 6.5ms -1. Calculate:
a) the potential energy lost by the tile.
b) The frictional force, assumed constant, which acts on the tile.
c) The coefficient of friction between the tile and the chute.
If Wendy pushes a tile from the top of the chute with a speed of 1.5ms-1 what is its speed at the
bottom?
17) Thomas the engine has a mass of 7.5 × 105kg and whilst traveling along a horizontal track he
experiences resistance to motion of magnitude 1.75 × 105N.
a) Calculate the force that Thomas produces when the acceleration is 1.5ms-2.
b) Calculate the power produced at the instant that Thomas is traveling at 12ms-1.
c) If Thomas then works at a constant rate of 600kW, find his greatest possible speed along the track
Harshana Perera(B.Sc,BIT,SCJP)
2014 R kit
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Physics
Work
18) Two masses are connected by a light string passing over a light frictionless
pulley, as shown in Figure P8.21. The mass m1 (which is greater than m2) is
released from rest. Using the law of conservation of energy, (a) determine the
speed of m2 just as m1 hits the ground in terms of m1, m2, and h, and (b) find the
maximum height to which m2 rises
19) A 5.00-kg block is set into motion up an inclined plane with an initial
speed of 8.00 m/s (Fig. P8.33). The block comes to rest after traveling
3.00 m along the plane, which is inclined at an angle of 30.0° to the
horizontal. For this motion determine (a) the change in the block’s
kinetic energy, (b) the change in the potential energy, and (c) the
frictional force exerted on it (assumed to be constant). (d) What is the
coefficient of kinetic friction?
20) 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?
21) A 3.00-kg block starts at a height h =60.0 cm on a plane that has an inclination angle of 30.0°, as shown in
Figure P8.39. Upon reaching the bottom, the block slides along a horizontal surface. If the coefficient of friction
on both surfaces is 0.200, how far does the block slide on the horizontal surface before coming to rest? (Hint:
Divide the path into two straight-line parts.)
Harshana Perera(B.Sc,BIT,SCJP)
2014 R kit
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