A luge and its rider, with a total mass of 90 kg, emerge from a downhill track o

Question

A luge and its rider, with a total mass of 90 kg, emerge from a downhill track onto a horizontal straight track with an initial speed of 41 m/s. Assume that they stop with a constant deceleration of 1.8 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 3.6 m/s2?
N

(e) What is d for a deceleration of 3.6 m/s2?
m

(f) What is W for a deceleration of 3.6 m/s2?
kJ

Explanation / Answer

Mass m = 90 kg Initial speed u = 41 m/ s Deceleration a= 1.8 m/ s 2 Final speed v = 0 Final speed v = 0 (a). Magnitude F is required for the decelerating force F = ma                                                                                      = 162 N (b) Distance d do they travel while decelerating d = ? From the relation v 2 - u 2 = 2ad                                      d = [ v 2 - u 2]/2a                                        = 466.94 m      We take a as negative (c) Work W is done on them by the decelerating force W = Fd                                                                                         = 75645 J                                                                                         = 75.645 kJ (d) F for a deceleration of 3.6 m/s 2 is F ' = m( 3.6)                                                                 = 324 N (e) d for a deceleration of 3.6 m/s 2 is   d = [ v 2 - u 2 ] / 2a' Where a ' = -3.6 m/ s 2
     d = 233.47 m (f) W for a deceleration of 3.6 m/s 2 is W = F'd                                                                  = 75.645 kJ

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