Question

The entrance of a rehabilitation center is at the elevation of 1.0 m and has a wheelchair ramp that is inclined 30 degrees relative to the horizontal. The mass of an average patient and the accompanying wheelchair is 110 kg, and the coefficient of static friction μs between the wheelchair wheels and the ramp is 0.60. Each wheel of the wheelchair has a mass of 3.0 kg and a radius of 0.40 m and can be modeled as a hoop rotating about its center. For the purposes of the following questions use g = 10 m/s2.

1.A patient applies the wheelchair brake on the ramp. In what direction does the force of friction point?
   The force of friction is zero.
   Perpendicular to the surface of the ramp
   Down the ramp
   Up the ramp

2. A patient applies the wheelchair brake on the ramp. When the brake is applied, the wheels are not blocked completely and they rotate relative to the chair with the patient and assume that the forces exerted by the brake on the wheels cause the wheels to be on the verge of slipping. What is the magnitude of the force of friction between the ramp and the wheelchair wheels?

	950 N
	330 N
	660 N
	570 N

3. A patient loses control of his wheelchair at the top of the ramp and rolls down without slipping. What is his speed at the bottom of the ramp? The patient does not apply brakes when he moves down the ramp.

	4.47 m/s
	4.41 m/s
	2.58 m/s
	4.35 m/s

4. When braking on the ramp, what is the magnitude of the frictional torque on the center of the wheel? When the brake is applied, the wheels are not blocked completely and they rotate relative to the chair with the patient and assume that the forces exerted by the brake on the wheels cause the wheels to be on the verge of slipping.

	66 N⋅m
	130 N⋅m
	290 N⋅m
	110 N⋅m

5. A patient loses control of his wheelchair at the top of the ramp and rolls down without slipping. What is his acceleration down the ramp? The patient does not apply brakes when he moves down the ramp.

	3.46 m/s2
	10 m/s2
	5 m/s2
	8.66 m/s2

6.How much work must a patient do to ascend the ramp at a constant speed?

	1100 J
	950 J
	-950 J
	-1100 J

Answer 1