Question

A 296-kg motorcycle is accelerating up along a ramp that is inclined 26.2° above the horizontal. The propulsion force pushing the motorcycle up the ramp is 3106 N, and air resistance produces a force of 286 N that opposes the motion. Find the magnitude of the motorcycle's acceleration.

Answer 1

The magnitude of the motorcycle's acceleration is 5.20 m/s².

Step-by-step explanation:

Given that,

Mass of motorcycle = 296 kg

Angle = 26.2°

Force on motorcycle= 3106 N

Force = 286 N

We need to calculate the magnitude of the motorcycle's acceleration

The net force acting on the motorcycle

Using newton's second law

`ma=F_(p)-F_(air)-F_(g)`

`ma=F_(p)-F_(air)-mg\sin\theta`

Put the value into the formula

`296a=3106-286-296*9.8*\sin26.2`

`a=(3106-286-296*9.8*\sin26.2)/(296)`

`a=5.20\ m/s^2`

Hence, The magnitude of the motorcycle's acceleration is 5.20 m/s².