Question

A luge and its rider, with a total mass of 85 kg, emerge from adownhill track onto a horizontal straight track with an initial speedof 37 m/s. if a force slows them to a stop at a constant rate of 2.0m/s2, (a) what magnitude f is required for the force, (b) what distanced do they travel while slowing, and (c) what work w is doneon them by the force? what are (d) f, (e) d, and (f) w if they, instead,slow at 4.0 m/s2?

Answer 1

(1)   Through the Second Law of motion, the equation  for Force is:

                                 F = m x a

Where m is mass and a is acceleration (deceleration)

 

(2)   Distance is calculated through the equation,

                             D = Vi^2 / 2a

Where Vi is initial velocity

(3)   Work is calculated through the equation,

                          W = F x D

 

Substituting the known values,

Part A:

(1)     F = (85 kg)(2 m/s^2) = 170 N

(2)     D = (37 m/s)^2 / (2)(2 m/s^2)  = 9.25 m

(3)     W = (170 N)(9.25 m) = 1572.5 J

 

Part B:

(1)    F = (85 kg)(4 m/s^2) = 340 N

(2)   D = (37 m/s)^2 / (2)(4 m/s^2) = 4.625 m

(3)    W = (340 N)(4.625 m) = 1572.5 J