How fast will the pebble be travelling with respect to the center of the wheel

In summary, the conversation discusses a physics problem involving a pebble stuck in a tire and the calculation of its speed when it is released tangentially. The conversation includes a proposed solution and a request for help in identifying the error in the calculation.
  • #1
huybinhs
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0

Homework Statement



A 24.6 g pebble is stuck in the thread of a 28.7 in tire. If the tire can exert an inward radial friction force of up to 19.3 N on the pebble, how fast will the pebble be traveling with respect to the center of the wheel when it flies out tangentiall?

Homework Equations



a = v^2 / r

The Attempt at a Solution



I got:

19.3 N = (m*v^2)/r => v^2 = (19.3 * r) / m = (19.3N * 0.36449 m) / 0.0246 kg = 16.9 m/s = final answer = INCORRECT ?

This problem is supposed to be easy, but I don't know what I'm doing wrong here. Anyone?
 
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  • #2
I can't see what's wrong with it.
 
  • #3

Related to How fast will the pebble be travelling with respect to the center of the wheel

What is the equation for calculating the speed of a pebble with respect to the center of a wheel?

The equation is v = rω, where v is the speed, r is the radius of the wheel, and ω is the angular velocity.

How does the angular velocity of the wheel affect the speed of the pebble?

The angular velocity directly affects the speed of the pebble. As the angular velocity increases, the speed of the pebble also increases. This is because the pebble is traveling a greater distance in the same amount of time.

Does the size of the pebble affect its speed with respect to the center of the wheel?

The size of the pebble does not directly affect its speed with respect to the center of the wheel. However, if the pebble is significantly larger than the wheel, it may cause friction and slow down the rotation of the wheel, which in turn would affect the pebble's speed.

How does the radius of the wheel affect the pebble's speed?

The radius of the wheel directly affects the pebble's speed. A larger radius will result in a higher speed, while a smaller radius will result in a lower speed. This is because the pebble is traveling a greater or lesser distance per rotation, respectively.

Can the pebble's speed with respect to the center of the wheel be negative?

No, the pebble's speed with respect to the center of the wheel cannot be negative. This is because the pebble is always traveling in a circular motion and its speed is always positive. A negative value would indicate that the pebble is traveling in the opposite direction, which is not possible in this scenario.

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