Rolling Motion, Pebble stuck in a Tire by Static Friction

In summary, the conversation is about a car with a 1.2 g pebble stuck in its tire tread, causing it to accelerate on a straight road. The maximum static friction holding the pebble in place is 3.6 N. The question asks for the speed of the car when the pebble flies out of the tread. The approach suggested involves using the centripetal force equation and rearranging for velocity, resulting in a speed of 16.88 m/s at the center of the wheel, which is half of the car's speed. The book answer is 17 m/s.
  • #1
lila.haj
8
0

Homework Statement



A 1.2 g pebble is stuck in a tread of a 0.76 m diameter automobile tire, held in place by static friction that can be at most 3.6 N. 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? I know the answer is 17 m/s however I don't know how to get it.

Homework Equations



v=(2*[itex]\pi[/itex]*R)/T
v=ωR
[itex]\alpha[/itex]=τ/I
I=1/2*M*R2
Fc=(m*v2)/2

The Attempt at a Solution



I tried using the centripetal force equation and rearranged for velocity, using the maximum static friction as my force. I then divided that number by 2 to get the speed in the centre of the wheel (since the speed at the top of the wheel is twice the speed of the vehicle).
 
Last edited:
Physics news on Phys.org
  • #2
I believe the approach suggested by the OP gives the correct answer.

F=(mv^2)/r
Rearrange for v...
V=SQRT(Fr/m)
= SQRT(3.6*0.38/0.0012)
= 33.76m/S

This is the Velocity of the top of the wheel. The Velocity of the car is half that..

33.76/2=16.88m/S

Book answer 17m/S.
 

1. What is rolling motion?

Rolling motion is a type of motion where an object, such as a wheel or a ball, moves and rotates simultaneously along a surface without slipping or sliding.

2. How does a pebble get stuck in a tire by static friction?

A pebble can get stuck in a tire by static friction when it gets wedged between the tire and the ground. The force of the tire rolling over the pebble creates a normal force, which in turn creates a frictional force that prevents the pebble from slipping out of the tire.

3. What is static friction?

Static friction is the force that resists the motion of an object when it is in contact with another surface and both are at rest relative to each other. It is the force that keeps the pebble stuck in the tire when the tire is not moving.

4. How does the pebble affect the rolling motion of the tire?

The pebble affects the rolling motion of the tire by creating an imbalance in the wheel. This can cause the tire to wobble or vibrate, which can affect the overall smoothness and efficiency of the rolling motion.

5. How can the pebble be removed from the tire?

The pebble can be removed from the tire by stopping the tire's rotation and manually removing the pebble. Alternatively, the tire can continue to roll and the pebble may eventually fall out due to the effects of friction and gravity.

Similar threads

Replies
24
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
8K
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
2
Replies
35
Views
2K
  • Introductory Physics Homework Help
Replies
15
Views
1K
  • Introductory Physics Homework Help
3
Replies
97
Views
3K
  • Introductory Physics Homework Help
Replies
4
Views
699
  • Introductory Physics Homework Help
Replies
19
Views
1K
  • Introductory Physics Homework Help
Replies
11
Views
3K
Back
Top