A 1000kg car accelerates from 3m/s East to 24m/s East at a rate of 3m/s. If the force of friction is 500N West; how much ower must the car exert?
If heat and mechanical losses make the car only 60% efficient, what total power must be exerted to accomplish the acceleration in 1st question.
To find the power required for the car to accelerate, we can use the equation for power:
Power = Force x Velocity
In this case, the force we need to consider is the net force acting on the car. The net force is the difference between the force exerted by the car in the east direction and the force of friction in the west direction.
Force exerted by the car = mass x acceleration
Given:
Mass of the car = 1000 kg
Initial velocity = 3 m/s east
Final velocity = 24 m/s east
Acceleration = rate of change of velocity = 3 m/s^2
Force of friction = 500 N west
First, let's find the force exerted by the car:
Force exerted by the car = mass x acceleration
= 1000 kg x 3 m/s^2
= 3000 N east
Next, let's find the net force:
Net force = Force exerted by the car - Force of friction
= 3000 N east - 500 N west
= 3500 N east
Now, let's calculate the power required:
Power = Force x Velocity
= Net force x Velocity
= 3500 N east x 24 m/s east
= 84000 W (or 84 kW)
Now, let's move to the second question. To find the total power required when the car is only 60% efficient, we need to account for the energy losses due to heat and mechanical losses.
Total power required = Power / Efficiency
= 84000 W / 0.6
= 140000 W (or 140 kW)
Therefore, the total power that must be exerted to accomplish the acceleration with 60% efficiency is 140 kW.