Answer to Question #178908 in Physics for Andu

Question

Determine the work done by the car engine during start-up, if the car moves at an acceleration of 2 m / s² for 10 s. The mass of the automobile is 1500 kg. The coefficient of motion friction is u = 0.02.

Answer 1

Let's first find the final velocity of the car:

$$v=v_0+at=0+2\ \dfrac{m}{s^2}\cdot10\ s=20\ \dfrac{m}{s}.$$

Then, we can find the distance traveled by the car:

$$d=\dfrac{1}{2}(v+v_0)t=\dfrac{1}{2}\cdot(20\ \dfrac{m}{s}+0)\cdot10\ s=100\ m.$$

Let's also find the net force acting on the car:

$$F_{net}=ma=1500\ kg\cdot2\ \dfrac{m}{s^2}=3000\ N.$$

Then, we can find the net work done by the force:

$$W_{net}=Fd=3000\ N\cdot100\ m=3\cdot10^5\ J.$$

Let's find the force of friction acting on the car:

$$F_{fr}=\mu mg=0.02\cdot1500\ kg\cdot9.8\ \dfrac{m}{s^2}=294\ N.$$

Then, we can find the work done by the force of friction:

$$W_{fr}=F_{fr}dcos\theta=294\ N\cdot100\ m\cdot cos180^{\circ}=-29400\ N.$$

Finally, we can find the work done by the car engine during start-up:

$$W_{net}=W_{eng}+W_{fr},$$ $$W_{eng}=W_{net}-W_{fr}=3\cdot10^{5}\ J-(-29400\ N)=3.294\cdot10^{5}\ J.$$