# Mass and Gravitational Potential Energy

Work done by a constant force

1-The drawing shows a plane diving toward the ground and then climbing back upward. During each of these motions, the lift force acts perpendicular to the displacement , which has the same magnitude, 1.7 × 103 m, in each case. The engines of the plane exert a thrust , which points in the direction of the displacement and has the same magnitude during the dive and the climb. The weight of the plane has a magnitude of 5.9 × 104 N. In both motions, net work is performed due to the combined action of the forces , and .

a.Is more net work done during the dive or the climb? Explain. b.Find the difference between the net work done during the dive and the climb.

Answer:

a. More net work is done during the dive.

b. 6.8 × 107 J

2- Find the work done by a force through a displacement of 3m in the positive x direction

Work-Energy theorem and kinetic energy

3-The mass of the space probe is 474-kg and its initial velocity is 275 m/s. If the 56.0-mN force acts on the probe through a displacement of 2.42×109m, what is its final speed?

Answer:

4-Example 2: Skier

Gravitational Potential Energy, Conservative versus Nonconservative Forces 5-The gymnast leaves the trampoline at an initial height of 1.20 m and reaches a maximum height of 4.80 m before falling back down. What was the initial speed of the gymnast?

Answer:

6-A man lifts a book of mass 0.45 kg at a constant speed from a shelf 1.2 m high to a shelf 2 m high 1) calculate:

a)The change in PE

b)The work done by the man

c)The work done by gravity

2) If the book falls down from the second shelf, calculate its speed as it passes the first shelf, and its speed when it hits the ground.

The Conservation of Mechanical Energy

7-A motorcyclist is trying to leap across the canyon by driving horizontally off a cliff 38.0 m/s. Ignoring air resistance, find the speed with which the cycle strikes the ground on the other side.

Answer:

8-The skateboarder in the drawing starts down the left side of the ramp with an initial speed of 5.4 m/s. If nonconservative forces, such as kinetic friction and air resistance, are negligible, what would be the height h of the highest point reached by the skateboarder on the right side of the ramp?

9-The drawing shows a person who, starting from rest at the top of a cliff, swings down at the end of a rope, releases it, and falls into the water below. There are two paths by which the person can enter the water. Suppose he enters the water at a speed of 13.0 m/s via path 1. How fast is he moving on path 2 when he releases the rope at a height of 5.20 m above the water? Ignore the effects of air resistance.

10-The figure below illustrates the motion of a mass m = 300 kg as it slides along a track, which has smooth segments (frictionless). If the mass was released from rest at point A on the track, fill the table below.

PEKEMEv

A

B

C

D

E

Nonconservative Forces and the Work–Energy Theorem

11-The 8 kg mass shown in the Figure moves 5 m up an inclined (θ = 30o) rough surface (μk= 0.2) as a result of the applied tension (T = 40N). If the mass started from rest and neglecting the masses of the pulley and the string, find:

a.The work done by the frictional force

b.The work done by gravitational force

c.The work done by tension

d.The speed of the object at the end of its motion

12-From point A to B on the rough surface, the cyclist lost 2000J of energy due to the frictional force of the rough surface of the 10 m road. She started with an initial speed vA at point A, arriving at point B with a speed of vB. The cyclist barely made it to the flat part (point C) of the frictionless surface without pedaling.

If the weight of the bike and the cyclist is 980N, and point C is located at h = 0.5 m above...

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