Object on an incline with friction

In summary, we have an object with a mass of 3 kg on a rough plane inclined at 45 degrees to the horizontal. The coefficient of friction is 0.2 and a force of 10 N is acting at 30 degrees relative to the object. To calculate the friction, we use the formula F = u R and find that the normal reaction is 26.2 N. However, there is a sign error and the cos 45 should be sin 45. With this correction, the answer should be 3.24 N. It is important to consider the direction and reference point when calculating forces.
  • #1
jinx007
62
0
An object of mass 3 kg lies on a rough plane inclined at 45 degree to the horizontal. The coefficient of friction is 0.2 and a force of 10 N acts at 30 degree to the object. Calculate the friction. According to the booklet the answer is 3.24 N

My work

F = u R


Normal reaction = 10 sin 30 + 30 cos 45 = 26.2

U = 0.2 x 26.2 = 5.24 N

I am confused HELPPPPPP.. where is the fault, is there something that i have not considered
 
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  • #2


What is the 30 degrees measured relative to? Is it relative to the plane the block is sitting on or relative to the horizontal?
 
  • #3


w3390 said:
What is the 30 degrees measured relative to? Is it relative to the plane the block is sitting on or relative to the horizontal?


It is relative to the block(object)
 
  • #4


So you have a block sitting on a slope. Is the block moving?
 
  • #5


Your normal reaction has a sign error. Also that cos 45 should be sin 45. I know numerically they are the same thing, but for what it actually represents, it should be sin.

I'll give you a hint, think about what the normal force is conceptually, not mathematically
 
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FAQ: Object on an incline with friction

1. What is the relationship between the angle of incline and the frictional force on an object?

The greater the angle of incline, the greater the frictional force acting on the object. This is because as the angle increases, the weight component of the object parallel to the incline also increases, resulting in a larger force pushing the object into the surface and creating more friction.

2. How does the coefficient of friction affect the motion of an object on an incline?

The coefficient of friction is a measure of the "roughness" of the surface between the object and the incline. A higher coefficient of friction means the surface is rougher and will result in a greater frictional force, making it harder for the object to move or slide down the incline. A lower coefficient of friction would result in less friction and the object would slide more easily.

3. What is the acceleration of an object on an incline with friction?

The acceleration of the object depends on the net force acting on it. In an ideal scenario with no friction, the acceleration would be equal to the component of the object's weight parallel to the incline. However, with friction, the acceleration will be less than this due to the opposing force of friction. The exact value can be calculated using Newton's second law, F=ma.

4. How does the mass of the object affect its motion on an incline with friction?

The mass of the object does not directly affect the frictional force acting on it, but it does affect the object's weight, which in turn affects the normal force and the component of weight parallel to the incline. Therefore, a heavier object would have a greater normal force and weight component, resulting in a larger frictional force and a slower acceleration.

5. Can an object ever reach a constant velocity on an incline with friction?

Yes, if the angle of incline and coefficient of friction are such that the frictional force is equal in magnitude to the component of weight parallel to the incline, the object will reach a constant velocity. This is known as the point of equilibrium, where the forces on the object are balanced and there is no net acceleration.

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