Mechanics Question -- Ball bearing on top of an accelerating car

In summary, the problem involves a ball bearing on a curved ramp on top of a car that is accelerating horizontally. The position of the ball relative to the ramp is used as a measure of the car's acceleration. To show that the acceleration is proportional to the horizontal distance moved by the ball, the ramp must be curved in the shape of a parabola. This can be expressed by finding the angle corresponding to a given acceleration and writing it in terms of a slope, as well as writing down the equation for a parabola in terms of a slope.
  • #1
JM samuel Liu
3
0

Homework Statement


  1. A ball bearing rests on a ramp fixed to the top of a car which is accelerating horizontally. The position of the ball bearing relative to the ramp is used as a measure of the acceleration of the car. Show that if the acceleration is to be proportional to the horizontal distance moved by the ball (measured relative to the ramp), then the ramp must be curved upwards in the shape of a parabola.

Homework Equations

The Attempt at a Solution


I sort of found out that the gradient at point of equilibrium is acceleration/ g but don't know if it's useful.[/B]
 
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  • #2
Can you start by showing what angle will correspond to a given acceleration? Can you write this in terms of a slope?

Can you write down the equation for a parabola in terms of a slope?
 
  • #3
DEvens said:
Can you start by showing what angle will correspond to a given acceleration? Can you write this in terms of a slope?

Can you write down the equation for a parabola in terms of a slope?

Please bear with me but...I think tan( angle) =a / g so angle = tan^1( a / g ) is probably what you want. I don't know what do you mean by writing it in terms of a slope...
 
  • #4
JM samuel Liu said:
Please bear with me but...I think tan( angle) =a / g so angle = tan^1( a / g ) is probably what you want. I don't know what do you mean by writing it in terms of a slope...
You need to get the slope and the bit about acceleration being proportional to position expressed in terms of x and y coordinates.
 

1. What is the purpose of a ball bearing on top of an accelerating car?

A ball bearing on top of an accelerating car is used to reduce friction and allow for smooth rotation of the wheels. This helps the car to move more efficiently and with less resistance.

2. How does the ball bearing on top of an accelerating car work?

The ball bearing works by using small metal balls to separate two surfaces and reduce friction. As the car accelerates, the ball bearing allows for the wheels to rotate freely and without resistance.

3. What happens if the ball bearing on top of an accelerating car is not functioning properly?

If the ball bearing is not functioning properly, it can cause increased friction and resistance, leading to decreased efficiency and potentially damaging the wheels and other components of the car.

4. Is it necessary to regularly maintain the ball bearing on top of an accelerating car?

Yes, it is important to regularly maintain the ball bearing to ensure it is functioning properly. This may include cleaning, lubricating, and replacing the bearing if necessary.

5. Can the ball bearing on top of an accelerating car affect the speed and performance of the car?

Yes, a faulty or poorly maintained ball bearing can affect the speed and performance of the car by increasing friction and resistance. This can result in slower acceleration and decreased efficiency.

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