A luge and its rider, with a total mass of 85 kg, emerge from a downhill track onto a horizontal straight track with an initial speed of 37 m/s. If a force slows them to a stop at a constant rate of 2.0 m/s2, (a) what magnitude F is required for the force, (b) what distance d do they travel while slowing, and (c) what work W is done on them by the force

a) 170N b) 342.25m c) 58.2KJ

Explanation:

a) magnitude F required for the force can be gotten using the Newton's second law of motion.

Force = mass × acceleration

Given mass = 85kg

acceleration =2.0m/s²

Force = 85×2

Force = 170N

Magnitude of force required is therefore 170N

b) To get the distance d at which they travel, we will use the equation of motion;

v² = u²+2ad where

v is the final velocity = 0m/s

u is the initial velocity = 37m/s

a is the acceleration = -2m/s² (since the body is slowing down while travelling)

d is the distance travelled while slowing

Substituting the values given into the formula we will have;

0² = 37²-2(2)d

-37² = -4d

d = 342.25m

c) Work done on them by the force can be calculated using the formula;

Work done = Force × Distance

Work done = 170×342.25

Work done = 58,182.5Joules

= 58.2KJ

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