Question

A motorcycle (mass of cycle plus rider = 2x 10^2 kg) is traveling at a steady speed of 20 m/s.?The force of air resistance acting on the cycle and rider is 2.1 102 N. Find the power necessary to sustain this speed under the following conditions.(a) the road is level W (b) the road is sloped upward at 35° with respect to the horizontal W

Answer 1

Answer:

$4.2\times10^3 W$  

$2.67\times 10^4 W$    

Explanation:

Given:

Mass of the rider plus the bike, $m=2\times10^2 kg$

Speed of the motorbike, u= 20 m/s

Force of resistance, $F=2.1\times10^2N$

Power necessary to sustain speed can be calculated as follows:

1. When road is level

Power = force x velocity  

P= F x u

$P=(2.1\times10^2N)(20 m/s) = 4.2\times10^3 W$

2. When the road is sloped at an angle 35°

An additional force will act due to component of gravity that is

$= mg sin \theta$

So,

$P = (F+mgsin\theta)u\\ P= (2.1\times10^2+2\times10^2\times 9.8 \times sin35^o)(20)=2.67\times 10^4 W$