Question

Two college students are sliding down a hill on excellent sleds so you can ignore friction. One has a mass of 85 kg and one has a mass of 75 kg. Which will reach the bottom of the hill first? a. they will both reach at the same time. b. 85 kg person c. 75 kg person

Answer 1

Answer:

a. They both reach at the same time.

Explanation:

On a frictionless incline, the only force that moves the person downwards is the x-component of the persons weight. (x-direction is the direction along the incline.)

$F = mg\sin(\theta)$

Here, θ is the angle of the incline above horizontal.

This force is equal to 'ma' according to Newton's Second Law.

Comparing the weights of the two persons gives

$F_1 = 85g\sin(\theta) = 85a_1\\F_2 = 75g\sin(\theta) = 75a_1\\a_1 = g\sin(\theta)\\a_2 = g\sin(\theta)$

Since the accelerations of both persons are the same, they reach the bottom at the same time.

The crucial point here is that the acceleration on a frictionless incline is independent from the mass of the object. If there were friction on the surface, then the person with smaller mass would reach the bottom first.