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luis00 · Oct 6, 2010, 01:55 PM

A car slides down an icy driveway that slopes at an angle of 10 degrees. What is the acceleration of the car?

-Can someone explain how to do this, I'm completely lost!

Unknown008 · Oct 7, 2010, 03:11 AM

The car is not running? If so, there is only one force acting on the car, which is gravity.

This is a picture I made. The force of gravity acts along the complete arrow pointing vertically downwards. However, not all the gravitational force is involved in the motion of the car. The component of this force, perpendicular to the plane contributes to the normal reaction of the car with the plane and the component acting along the plane contributes to the motion of the car.

So, the force acting on the car is given by: $mgsin\theta$

From W = mg (where m is the mass of the car and g the acceleration due to gravity, which is 9.8 m/s^2)

Why sin theta?

Because $sin\theta = \frac{opp}{hyp}$

If you look at one of the triangle of forces which the gravitational force makes, mg is the hypotenuse.

Then, since $sin\theta = \frac{F_p}{mg}$

The force parallel to the plane, Fp is given by mg sin theta.

So, you have the force ( $mgsin\theta$ ).

You know that F = ma.

So, you get:

$mgsin\theta = ma$

Find a.

I hope it helps! :)

luis00 · Oct 7, 2010, 08:13 PM

Thanks for your response. If I use mgsin=ma then how do I find the mass if it's not given?

Unknown008 · Oct 7, 2010, 11:50 PM

Well, the beautiful thing in this is that the mass is not necessary! You will see that mass will cancel out. :)