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# Patients in a wheelchair

## Problem

A hospital is considering revamping its rehabilitation center. In an effort to facilitate movement for handicapped individuals, administrators commissioned a project to reconstruct a specific ramp. Preliminary investigations involved three volunteer patients wheeling their way up the ramp individually and providing feedback on the difficulty of the exercise.
Figure 1. A diagram of the ramp under consideration for reconstruction.
The hospital is further interested in obtaining better wheelchairs. The hospital staff is pursuing qualities such as improved balance, weight, torque, and wheel grip. To consolidate this entire project, they requested the patient volunteers to each use a different wheelchair under consideration for widespread hospital use during their trial.
Wheelchair A has a frame composed of aluminum and has thin rubber wheels. On the other hand, wheelchair B is made of plastic and has thicker rubber wheels. Finally, wheelchair C has increased rigidity due to its titanium build and large leather wheels.
Information involving each wheelchair’s mass, type, and coefficient of friction is compiled in Table 1.
Table 1. Compilation of wheelchair data.
MassWheel materialμ${}_{s}$μ${}_{k}$
Wheelchair A20kgThin rubber.5.2
Wheelchair B20kgThick rubber.6.3
Wheelchair C30kgLeather.7.4
The masses of volunteers A, B, and C are 60, 50, and 70kg respectively.
Table 2. Trigonometric function table of angles 30 and 45 degrees.
Anglesinθcosθtanθ
30${}^{\circ }$0.50.870.6
45${}^{\circ }$0.70.71
Volunteer B makes her way up the ramp on wheelchair B. She pauses and engages her brakes to catch her breath. What is the force of friction exerted on the wheelchair while at rest on the ramp? (Use 10 m/s${}^{2}$ for the acceleration due to gravity)
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