Question

1) A cart for hauling ore out of a gold mine has a mass of 447 kg, including its load. The cart runs along a straight stretch of track that climbs a shallow 4.63∘ incline. A donkey, which is trudging along and to the side of the track, has the unenviable job of pulling the cart up the slope with a 436 N force for a distance of 115 m by means of a rope that is parallel to the slope but makes an angle of 12.7∘ with the track.

Model the rolling resistance of the cart as though it were sliding on the track with a coefficient of friction of 0.0163. Use ?=9.81 m/s2, and note that angle A in the image is the angle of the incline while angle B is the angle the rope makes with the track

Find the work ?d that the donkey performs on the cart during this process.

Find the work ?g that the force of gravity performs on the cart during this process.

Calculate the work ?f done on the cart by friction during this process.

2) Steven carefully places a ?=1.55 kg wooden block on a frictionless ramp so that the block begins to slide down the ramp from rest. The ramp makes an angle of ?=58.3° up from the horizontal.

Which forces do nonzero work on the block as it slides down the ramp?

- Spring

- Friction

- Normal

- Gravity

How much total work has been done on the block after it slides down along the ramp a distance of 1.85 m?

Total work done on the block:        J

Nancy measures the speed of the wooden block after it has gone the 1.85 m down the ramp. Predict what speed she should measure.

Final speed after sliding from rest:        m/s

Now, Steven again places the wooden block back at the top of the ramp, but this time he jokingly gives the block a big push before it slides down the ramp. If the block's initial speed is 2.00 m/s and the block again slide down the ramp 1.85 m, what should Nancy measure for the speed of the block this time?

Final speed after sliding with initial speed 2.00 m/s:         m/s

3) Suppose that the average U.S. household uses 14600 kWh (kilowatt‑hours) of energy in a year. If the average rate of energy consumed by the house was instead diverted to lift a 1360 kg car 17.8 m into the air, how long would it take?

Car:          s

Using the same rate of energy consumption, how long would it take to lift a loaded Boeing 747 airplane, with a mass of 4.15×105 kg, to a cruising altitude of 9.92 km?

Airplane:          s

Answer 1