A luge and its rider, with a total mass of 88 kg, emerge from a downhill track o

Question

A luge and its rider, with a total mass of 88 kg, emerge from a downhill track onto a horizontal straight track with an initial speed of 30 m/s. Assume that they stop with a constant deceleration of 2.2 m/s2

. (a) What magnitude F is required for the decelerating force? N

(b) What distance d do they travel while decelerating? m

(c) What work W is done on them by the decelerating force? kJ

(d) What is F for a deceleration of 4.4 m/s2? N

(e) What is d for a deceleration of 4.4 m/s2? m

(f) What is W for a deceleration of 4.4 m/s2? kJ

Explanation / Answer

m = 88 kg, u = 30 m/s,v =0, a = 2.2 m/s^2

(a) F = ma = 88*2.2 = 193.6 N

(b) from kinematci equation

v^2 - u^2 = 2as

0 - 30^2 = -2*2.2*d

d = 204.5 m

(c) W = F.d = 193.6*204.5 = 39.6 kJ

(d) a = 4.4 m/s^2

F = ma = 88*4.4 = 387.2 N

(e) from kinematci equation

v^2 - u^2 = 2as

0 - 30^2 = -2*4.4*d

d = 102.273 m

(f) W = F.d = 387.2*102.273 = 39.6 kJ

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