The person in the figure below weighs 176 lb. Each crutch makes an angle of ? =

Question

The person in the figure below weighs 176 lb. Each crutch makes an angle of ? = 27.0

The person in the figure below weighs 176 lb. Each crutch makes an angle of ? = 27.0 A degree with the vertical (as seen from the front). Half of the person's weight is supported by the crutches, the other half by the vertical forces exerted by the ground on his feet. Assuming he is at rest and the force exerted by the ground on the crutches acts along the crutches, determine each of the following. (a) the smallest possible coefficient of friction between crutches and ground (b) the magnitude of the compression force supported by each crutch

Explanation / Answer

partA:

friction = tan theta

so here friction u = tan 27

u = 0.51

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the two crutches together Support half of the weight

Let F be the force along the crutch, so splitting them in Vertical and Horizontal forces

Fh and Fv

Fv is the half of the weight of the person

so

Fv = F sin theta

here F = 176 lb = 176*4.448 = 782.848 N

so

Fv = Fsin theta = 782.848

Force F = 782.848/sin 27

F = 1724.3 N

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