A scooter and rider are moving along a bumpy road with a coefficient of friction of .81. The mass of the scooter is 35 kg and the rider's mass is 15 kg.

Question

What force is needed to accelerate the scooter and rider at 5 m/s² ?

If the rider falls off and the same force is applied, what is the new acceleration of the scooter alone?

Answer 1

First question:

M = mass of scooter

m = mass of rider

μ = coefficient of friction

a = acceleration

F = applied force (what you want to solve for)

You want the net force to equal (m + M)a.

F - μ(m + M)g = (m + M)a

F = (m + M)(μg + a)

Plug in the numbers and evaluate F.

Second question:

F is the same, but the mass of the system is just the mass of the scooter.

F - μMg = Ma₁

a₁ = (F - μMg) / M

Plug in the numbers and evaluate a₁.

Answer 2

The total weight is (35+15)•(9.8) = 490N, which leads to a frictional force of 396.1N. To accelerate a 50 kg weight at 5 m/s^2, you need a 250N forward force. So the forward force needed is 646.1N.

If the rider falls off, then the new net force on the scooter is 646.1N - 35•9.8•0.81 = 396.9N, which causes a 396.9/35 = 11.34 m/s^2 acceleration.