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

Answer:

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

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

$296a=3106-286-296\times9.8\times\sin26.2$

$a=\dfrac{3106-286-296\times9.8\times\sin26.2}{296}$

$a=5.20\ m/s^2$

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