# Solving Friction Force Between Plank & Sphere

• ritwik06
In summary, a uniform solid sphere of mass m and radius R is placed on a plank of mass m on a smooth surface. A force F is applied at an angle of 45 degrees to the horizontal at the top of the sphere. The surface between the plank and the sphere is rough with no slipping. Using torque equations and assuming the friction force on the sphere points to the right, we can solve for the force of friction between the plank and the sphere to be -F/3√2, with the friction force pointing left due to the sphere dragging the plank to the right.
ritwik06

## Homework Statement

A plank of mass m is placed on a smooth surface. Now a uniform solid sphere of mass m and radius R is placed on the plank as shown in the figure. A force F is applied at top most point of the sphere at an angle of 45 to the horizontal. Surface between the plank and the sphere is extremely rough so that there is no slipping. Find the force of friction acting between the plank and the sphere.

http://img76.imageshack.us/img76/7259/diagin7.jpg

## The Attempt at a Solution

This is the diagram I drew:
I considered only the necessary forces. Normals have been omitted.
http://img82.imageshack.us/img82/3304/freebodydiagramoa9.jpg

By torque equation:
$$(F/\sqrt{2}+Fr)*R=2/5 MR^{2}* a/R$$

I can write angular acceleration with respect to plank as a/R, since the boy does not skid.
$$(F/\sqrt{2}+Fr)=ma1$$
a1 is acceleration with respect to ground.

a1=a- Fr/m

I solve these 3 equations and I got$$Fr= -3F/\sqrt{2}$$
but the correct answer given seems like $$Fr= -F/3\sqrt{2}$$
An I also have one more confusion: Why is friction force coming out to be negative?

Last edited by a moderator:
ritwik06 said:
By torque equation:
$$(F/\sqrt{2}+Fr)*R=2/5 MR^{2}* a/R$$

I can write angular acceleration with respect to plank as a/R, since the boy does not skid.
$$(F/\sqrt{2}+Fr)=ma1$$
a1 is acceleration with respect to ground.
These equations aren't consistent. If, as you assumed, the friction on the sphere points to the right, then it exerts a torque opposite to that of the applied force.

An I also have one more confusion: Why is friction force coming out to be negative?
The sphere drags the plank to the right, thus the friction force on the sphere points left.

## 1. What is friction force and why does it occur?

Friction force is the resistance that occurs when two objects rub against each other. It is caused by microscopic bumps and imperfections on the surfaces of the objects, which create resistance and make it difficult for the objects to slide past each other.

## 2. How does friction force affect the movement of a plank and sphere?

The friction force between a plank and sphere can either help or hinder the movement of the objects, depending on the direction of the force. If the force is parallel to the surface of the objects, it will help the objects slide past each other. However, if the force is perpendicular to the surface, it will prevent the objects from moving.

## 3. How can the friction force between a plank and sphere be calculated?

The friction force can be calculated using the formula F = μN, where F is the friction force, μ is the coefficient of friction, and N is the normal force between the objects. The coefficient of friction is a measure of how rough or smooth the surfaces of the objects are, and it varies depending on the materials in contact.

## 4. What factors can affect the friction force between a plank and sphere?

The friction force between a plank and sphere can be affected by several factors, such as the roughness of the surfaces, the weight of the objects, and the presence of any lubricants. The type of material and temperature can also play a role in the amount of friction force between the objects.

## 5. How can the friction force between a plank and sphere be reduced?

The friction force between a plank and sphere can be reduced by using a lubricant, such as oil or grease, to create a slippery layer between the surfaces. Additionally, using smoother materials or polishing the surfaces can also reduce friction. Adjusting the weight or angle of the objects can also affect the amount of friction force present.

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