Answer to Question #178908 in Physics for Andu

Question #178908

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.


1
Expert's answer
2021-04-07T10:09:13-0400

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


v=v0+at=0+2 ms210 s=20 ms.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=12(v+v0)t=12(20 ms+0)10 s=100 m.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:


Fnet=ma=1500 kg2 ms2=3000 N.F_{net}=ma=1500\ kg\cdot2\ \dfrac{m}{s^2}=3000\ N.

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


Wnet=Fd=3000 N100 m=3105 J.W_{net}=Fd=3000\ N\cdot100\ m=3\cdot10^5\ J.

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


Ffr=μmg=0.021500 kg9.8 ms2=294 N.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:


Wfr=Ffrdcosθ=294 N100 mcos180=29400 N.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:


Wnet=Weng+Wfr,W_{net}=W_{eng}+W_{fr},Weng=WnetWfr=3105 J(29400 N)=3.294105 J.W_{eng}=W_{net}-W_{fr}=3\cdot10^{5}\ J-(-29400\ N)=3.294\cdot10^{5}\ J.

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