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The Problem:

(a) A car of mass m is on an icy driveway inclined at an angle of 20$^{\circ}$, Determine the acceleration of the car, assuming that the incline is frictionless.

The questions is followed with an answer:

(a) 3.35 m/s^2

When I worked the problem I set up a free body-diagram with the normal force pointed upwards on the y-axis and the force of gravity in the 4th quadrant at a 20$^{\circ}$ to the y-axis.

However, without knowing the mass of the car I could not solve the problem. Does the mass not matter or was this just an error on part of the book?

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The force on the car (due to gravity) is proportional to the mass.

The inertia of the car is also proportional to the mass.

If you set up your solution properly you should see the two terms cancel out. You never need to know the force - you are asked about the acceleration (which is force divided by mass).

Put differently: the acceleration due to gravity along the slope is some geometric factor times the gnormal (vertical) gravitational acceleration. You can compute this without knowing the mass of the car.

Can you take it from here?

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  • $\begingroup$ Thanks for the help! I wrote that the sum of all forces in the x-direction is 0; however, it is ma. If I solve for a, the m's cancel out. $\endgroup$ – Rhendz Nov 8 '14 at 22:54

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