Work, Energy and Power
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12 Work, Energy and Power
18 A bead of mass m = 5.00 kg is released from point ○
A and slides on the
frictionless track as shown.
Determine
(a) the bead’s speed at points ○
B and ○
C , and
(b) the work done by the force of gravity in moving the bead from ○
A to ○
C.
19 A bead slides without friction around a loop-the-loop of radius R = 0.20 m.
If the bead is released from a height h = 0.70 m, what is its speed at point A?
Work, Energy and Power
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20 A ball was thrown vertically up with speed u = 12 m s–1 from a height 15 m
above the sea-level as shown. Ignore air resistance.
u
15 m
sea
(a) Use the equation “v 2 = u 2 + 2as” to find the speed of the ball as it hits the
sea. Why can this equation be used in this problem?
(b) Solve (a) using the conservation of mechanical energy. Explain why the
conservation law can be used in this question.
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21 A skier slides down a smooth slope as shown.
u
Her velocity at ○
A is u = 2.0 m s–1.
(a) Find her velocity at ○
B .
(b) Why can’t we use the equation “v 2 = u 2 + 2as” when solving (a)?
22 A man jumped up, his lift-off velocity vcm is 3.2 m s–1.
CM = centre of mass
Find H, the maximum height increase.
Work, Energy and Power
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23 A powerful grasshopper launches itself at an angle of 45 above the
horizontal and rises to a maximum height of 1.00 m during the leap.
With what speed vi did it leave the ground? Neglect air resistance.
24 A block having a mass of 0.80 kg is given
an initial velocity vA = 1.2 m s–1 to the right
and collides with a spring of negligible
mass and force constant k = 50 N m–1.
Assuming frictionless surface, find
(a) vB when xB = 0.10 m,
(b) the maximum compression xmax.
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25 A 50.0-kg circus acrobat drops from a height of 2.00 m straight down onto a
springboard with a force constant of 8.00  103 N m–1, as shown.
By what maximum distance does she compress the spring?
26 An object of mass 3.0 kg starts from rest and slides a distance 2.0 m down a
frictionless incline of angle 30. It contacts an unstressed spring of negligible
mass and force constant 440 N m–1.
2.0 m
2.0 m
x
30
initially
30
finally
The object slides an additional distance x as it is brought momentarily to rest
by compression of the spring. Find x.
Work, Energy and Power
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27 A child’s pogo stick stores energy in a spring with a force constant of
2.50  104 N m–1.
h
0.100 m
At position ○
A , the spring compression is a maximum and the child is
B , the spring is relaxed and the child is
momentarily at rest. At position ○
C , the child is again momentarily at rest at the
moving upward. At position ○
top of the jump. The combined mass of child and pogo stick is 25.0 kg.
B .
(a) Calculate the speed of the child at ○
(b) Determine h.
(c) Calculate the child’s maximum upward speed.
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28 A bored college student decides to try bungee jumping. He attaches an
elastic bungee cord to his ankles and happily jumps off a tall bridge across a
river. He ends up barely touching the water before the cord jerks him back up.
The student has a mass of 75 kg and falls a distance of 41 m before the
elastic rope attached to him starts to exert any force on him. The total
distance of fall for the student before he stops for the first time is 73 m.
(a) Find the force constant of the elastic rope.
(b) Calculate how far the student has fallen from the top when he has
maximum kinetic energy.
(c) Find the maximum kinetic energy of the student during the fall.
Work, Energy and Power
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Connected Bodies
When two bodies are connected, we need to consider the total mechanical
energy of the bodies as a whole rather than as individual bodies.
29
Two objects are connected by a light string passing over a light frictionless
pulley as shown in the diagram. The object of mass 5.00 kg is released from
rest. Using the principle of conservation of energy, find
(a) the speed of the 3.00-kg object just as the 5.00-kg object hits the ground,
(b) the maximum height (above ground) to which the 3.00-kg object rises.
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