A 1.1 pebble is stuck in a tread of a 0.85 diameter automobile tire, held in place by static friction that can be at most 3.9 . The car starts from rest and gradually accelerates on a straight road.How fast is the car moving when the pebble flies out of the tire tread?
To determine the speed of the car when the pebble flies out of the tire tread, we can use the concept of centripetal force. The pebble is stuck in the tread of the tire due to static friction, which provides the necessary centripetal force to keep the pebble moving in a circular path.
The maximum static friction force that can be exerted on the pebble is given as 3.9 N. This maximum static friction force is also the maximum centripetal force acting on the pebble.
The centripetal force is given by the formula: F = m * (v^2/r), where F is the force, m is the mass of the object, v is the velocity, and r is the radius of the circular path.
We can substitute the maximum static friction force (3.9 N) for F, the mass of the pebble (1.1 kg) for m, and the radius of the tire (0.85/2 = 0.425 m) for r.
Now we can solve the equation to find v:
3.9 = 1.1 * (v^2/0.425)
Rearranging the equation, we have:
(v^2/0.425) = 3.9/1.1
v^2 = (3.9/1.1) * 0.425
v^2 ≈ 5.943
Taking the square root of both sides, we find:
v ≈ √5.943
v ≈ 2.44 m/s
Therefore, the car is moving at approximately 2.44 m/s when the pebble flies out of the tire tread.