Question number 1: A 68kg bike racer climbs a 1100m -long section of road that h

Question

Question number 1:

A 68kg bike racer climbs a 1100m -long section of road that has a slope of 4.3(degree).
By how much does his gravitational potential energy change during this climb?
Express your answer to two significant figures and include the appropriate units.

Question number 2:
A car is parked at the top of a 52m -high hill. It slips out of gear and rolls down the hill.
How fast will it be going at the bottom? (Ignore friction.)
Express your answer using two significant figures.

Question number 3:
A 10kg runaway grocery cart runs into a spring with spring constant 290N/m and compresses it by 80cm.
What was the speed of the cart just before it hit the spring?
Express your answer using two significant figures.

Question number 4:
What minimum speed does a 100 puck need to make it to the top of a 4.3 -long, 25 frictionless ramp?

(in m/s)

Explanation / Answer

1. He will reach a height of 1100sin(4.3) meters = 82.4755 m
Potential energy = mgh = 68(9.8)(82.4755) = 54962.4 J increase

2. initial potential energy = mgh = 52(9.8)m = 509.6m J
U = Kfinal = 1/2mv2

509.6m = .5mv2

v = 31.925 m/s

3. 1/2kx2 = potential energy spring = (.5)290(.8)2 = 1/2(10)v2

18.56 = v2

v = 4.3 m/s

(I'll do the last one in a little bit)

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