What is the linear speed of a block with friction inside a cylinder?

In summary, the problem involves a 200 g block inside a cylinder with a diameter of 1m and a coefficient of friction of 0.5. The goal is to find the linear speed of the block. After considering the forces acting on the object, the solution involves using the formula v = ωr and setting the net force equal to zero. With the correct direction of friction, the final formula becomes v = √((μmg + 2mg)/mr).
  • #1
harimakenji
94
0

Homework Statement


a 200 g block placed inside a cylinder (attached to the curve surface, not the base or top of the cylinder) with diameter 1m. If the coefficient of friction is 0.5, find the linear speed of the block.

Homework Equations


v = ωr

The Attempt at a Solution


I do not know how to take friction into consideration when doing this problem. When I draw the free body diagram, there are 3 forces acting on the object: the normal force directed radially inward, the friction directed tangentially, and weight directed downward.
So, normal force = mv2/r. After that, I do not know how to continue.

Thank you very much

******
just edit my post
I just realized that the direction of friction is wrong. It should be upward. I've solved this problem
 
Last edited:
Physics news on Phys.org
  • #2
with the following steps: Fnet = Fn - Ff - W = mv2/r - μmg - mg = 0v2 = (μmg + 2mg)/mrv = √((μmg + 2mg)/mr)
 

1. What is centripetal force with friction?

Centripetal force with friction is a force that acts towards the center of a circular path and is caused by the friction between an object and the surface it is moving on. This force is necessary to keep an object moving in a circular path with a constant speed.

2. How is centripetal force with friction different from centripetal force without friction?

Centripetal force with friction and centripetal force without friction are similar in that they both act towards the center of a circular path, but the difference lies in the cause of the force. Centripetal force without friction is caused by a tension or gravitational force, while centripetal force with friction is caused by the friction between an object and the surface it is moving on.

3. How is the magnitude of centripetal force with friction determined?

The magnitude of centripetal force with friction can be determined by using Newton's second law of motion, which states that force is equal to mass times acceleration. In this case, the acceleration is centripetal acceleration, which can be calculated using the formula a = v^2/r, where v is the velocity of the object and r is the radius of the circular path. The force can then be calculated by multiplying the mass of the object by the centripetal acceleration.

4. What role does friction play in centripetal force with friction?

Friction plays a crucial role in centripetal force with friction as it is the force that enables the object to maintain a circular path. Without friction, the object would not experience a force towards the center of the circle and would continue moving in a straight line.

5. Can centripetal force with friction ever be greater than the force of friction?

Yes, it is possible for centripetal force with friction to be greater than the force of friction. This can occur when the object is moving at a high speed or when the radius of the circular path is small. In these cases, the centripetal force must be greater in order to overcome the force of friction and maintain the circular motion.

Similar threads

Coefficient of kinetic friction of a block sliding across the ceiling
    • Introductory Physics Homework Help
Replies
7
Views
341
Ratio of acceleration of two solid cylinders released on two inclined planes
    • Introductory Physics Homework Help
Replies
22
Views
1K
Newton's laws — Two stacked blocks sliding on a frictionless floor
    • Introductory Physics Homework Help
Replies
17
Views
2K
A-level Maths Mechanics: Prevent Block from Sliding Down Inclined Plane
    • Introductory Physics Homework Help
Replies
30
Views
2K
What will the FBD of 2 blocks being pulled look like?
    • Introductory Physics Homework Help
Replies
7
Views
1K
Direction of friction in circular motion
    • Introductory Physics Homework Help
Replies
5
Views
2K
A block placed in a horizontal hollow cylinder
    • Introductory Physics Homework Help
Replies
4
Views
3K
Free body Diagram of a Plank resting on two Cylinders
    • Introductory Physics Homework Help
Replies
14
Views
2K
Plotting the graph of Friction Force vs. time (Laws of motion)
    • Introductory Physics Homework Help
Replies
1
Views
1K
Pulleys with friction , FORCES
    • Introductory Physics Homework Help
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top