Posted by **Sonya** on Saturday, September 19, 2009 at 11:48am.

A car is traveling over the top of a hill, which we will model to be a piece of a circular arc of radius R. For each case below, draw careful to-scale motion maps and use them to construct the velocity vectors at the following three points: the top of the hill; equal time intervals on either side of the hill. Use the latter two velocity vectors to construct the average acceleration vector a at the top of the hill. Evaluate and comment on the direction and relative magnitude of a for the following cases:

(a) The car is moving at constant speed v over a hill of radius R.

(b) The car is moving at constant speed 2v. Quantitatively, how does the magnitude a change compared to that in part (a)?

(c)The car is moving at constant speed v over a hill of radius R/2. Quantitatively, how does a now compare to that obtained in part (a)?

(d)Brownie points:From your results of parts (a)-(c), obtain an expression for the magnitude of the acceleration for the case of uniform circular motion (constant speed). Hint: what variables could the acceleration depend on? There is only one possible combination of those variables that will give you the right units!And your graphical constructions in parts (a)-(c) should confirm the functional dependences.

(e)The car speeds up as it goes over the top of the hill; the car slows down as it goes over the top of the hill. Discuss your results for this non-uniform circular motion in the context of the “superposition principle:” the idea that a seemingly complex motion (accelerating over a hill) can be broken down into the superposition (addition) of two simpler motions – perhaps better described here as a decomposition.

## Answer this Question

## Related Questions

- Physics - A stuntman drives a car over the top of a hill, the cross section of ...
- physics hw - A 300. kg roller coaster car is traveling at a constant speed of 15...
- physics circular arc - A motorcycle is traveling up one side of a hill and down ...
- physics - the occupants of a car traveling at 25.7 m/s become weightless for an ...
- physics - A roller-coaster car has a mass of 1100 kg when fully loaded with ...
- Physics - a car goes over a circular hill of 50m radius at a constant speed of ...
- Physics - a car goes over a circular hill of 50m radius at a constant speed of ...
- Science - A car speeds over the top of a hill. If the radius of curvature of the...
- physics - In the figure below, a stuntman drives a car (without negative lift) ...
- physics - A motorcycle is traveling up one side of a hill and down the other ...

More Related Questions