9. Work & Energy

Net Work & Work-Energy Theorem

Open Question
The cable of a crane is lifting a 750 kg girder. The girder increases its speed from 0.25 m/s to 0.75 m/s in a distance of 3.5 m. (a) How much work is done by gravity?
Open Question
A pile driver lifts a 250 kg weight and then lets it fall onto the end of a steel pipe that needs to be driven into the ground. A fall from an initial height of 1.5 m drives the pipe in 35 cm. What is the average force that the weight exerts on the pipe?
Open Question
CALC A 2.6 kg block is attached to a horizontal rope that exerts a variable force Fx=(20−5x) N, where x is in m. The coefficient of kinetic friction between the block and the floor is 0.25. Initially the block is at rest at x=0 m . What is the block's speed when it has been pulled to x=4.0 m?
Open Question
The maximum energy a bone can absorb without breaking is surprisingly small. Experimental data show that a leg bone of a healthy, 60 kg human can absorb about 200 J. From what maximum height could a 60 kg person jump and land rigidly upright on both feet without breaking his legs? Assume that all energy is absorbed by the leg bones in a rigid landing.
Open Question
A 20 kg child is on a swing that hangs from 3.0-m-long chains. What is her maximum speed if she swings out to a 45 degree angle?
Open Question
In a hydroelectric dam, water falls 25 m and then spins a turbine to generate electricity. (a) What is (delta)Ug of 1.0 kg of water?
Open Question
A cable with 20.0 N of tension pulls straight up on a 1.50 kg block that is initially at rest. What is the block's speed after being lifted 2.00 m? Solve this problem using work and energy.
Open Question
A 1500 kg car traveling at 10 m/s suddenly runs out of gas while approaching the valley shown in FIGURE EX10.11. The alert driver immediately puts the car in neutral so that it will roll. What will be the car's speed as it coasts into the gas station on the other side of the valley? Ignore rolling friction.
Open Question
A pendulum is made by tying a 500 g ball to a 75-cm-long string. The pendulum is pulled 30 degree to one side, then released. What is the ball's speed at the lowest point of its trajectory?
Open Question
A 55 kg skateboarder wants to just make it to the upper edge of a 'quarter pipe,' a track that is one-quarter of a circle with a radius of 3.0 m. What speed does he need at the bottom?
Open Question
A system of two objects has (delta)Ktot = 7J and (delta)U = -5J. (a) How much work is done by interaction forces?
Open Question
(II) A 66.5-kg hiker starts at an elevation of 1150 m and climbs to the top of a peak 2660 m high.

(c) Can the actual work done be greater than this? Explain.
Open Question
(II) A 66.5-kg hiker starts at an elevation of 1150 m and climbs to the top of a peak 2660 m high.
(b) What is the minimum work the hiker must do?
Open Question
An airplane pilot fell 370 m after jumping from an aircraft without his parachute opening. He landed in a snowbank, creating a crater 1.1 m deep, but survived with only minor injuries. Assuming the pilot’s mass was 82 kg and his terminal velocity was 45 m/s, estimate:
(a) the work done by the snow in bringing him to rest; .
Open Question
Stretchable ropes are used to safely arrest the fall of rock climbers. Suppose one end of a rope with unstretched length ℓ is anchored to a cliff and a climber of mass m is attached to the other end. When the climber is a height ℓ above the anchor point, he slips and falls under the force of gravity for a distance 2ℓ , after which the rope becomes taut and stretches a distance x as it stops the climber (see Fig. 7–37). <IMAGE>

Assume a stretchy rope behaves as a spring with spring constant k.

(a) Applying the work-energy principle, show that

x = mg/k [ 1 + √1 + (4kℓ/mg)]