Frictional Forces Physics 1 Problem

In summary: The tension points along the rope doesn't it? Why would the rope care about what angle stuff is attached to it?The tension in the rope is also dependent on the angle of the first mass to the second mass.
  • #1
Almost935
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Homework Statement



7.) A 1520-N crate is to be held in place on a ramp that rises at 30.0° above the horizontal (see figure). The massless rope attached to the crate makes a 22.0° angle above the surface of the ramp. The coefficients of friction between the crate and the surface of the ramp are µk = 0.450 and μs = 0.650. The pulley has no appreciable mass or friction. What is the MAXIMUM weight w that can be used to hold this crate stationary on the ramp?

Picture of problem:
attachment.php?attachmentid=67399&stc=1&d=1394245127.png


Homework Equations



Fs = μsFn

F = ma

The Attempt at a Solution



I attempted by first mapping out the forces for Fx and Fy. I then solved for the normal force in order to replace it in the static friction force equation so as to be able to solve for the tension in the rope which I then found to be 1380 N. I am unsure whether this is the answer. Logically it somewhat makes sense that the tension in the rope must be equal to the weight of the mass on the other end to be completely still. Looking for some analysis of my answer and some pointers in the correct direction
 

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  • #2
Almost935 said:
I attempted by first mapping out the forces for Fx and Fy.
Guessing that you placed the axes to that +x direction points "up along the ramp"?

I then solved for the normal force in order to replace it in the static friction force equation so as to be able to solve for the tension in the rope which I then found to be 1380 N. I am unsure whether this is the answer. Logically it somewhat makes sense that the tension in the rope must be equal to the weight of the mass on the other end to be completely still.
Best practice is to do all the algebra before you put numbers in - it can avoid the sort of confusion you ended up in.

Looking for some analysis of my answer and some pointers in the correct direction
You need two free-body diagrams to be sure to get this answer correct, one for the mass on the slope - which you have basically done, and the other for the hanging mass.

This gives you two equations - which is good, because you have two unknowns: the tension in the rope and the weight that hangs off the pulley.

So repeat the process for the hanging mass and see if you are right.
 
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  • #3
So you are saying that the Tension is equal throughout despite the angle on the first mass?
 
  • #4
The tension points along the rope doesn't it? Why would the rope care about what angle stuff is attached to it?
 
  • #5
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I would like to commend you for your attempt at solving this problem. Your approach of mapping out the forces and using the equations Fs = μsFn and F = ma is a good start. However, there are a few things to consider in order to arrive at the correct answer.

Firstly, it is important to note that in this problem, there are two types of frictional forces at play - static friction and kinetic friction. Static friction occurs when the crate is at rest and kinetic friction occurs when the crate is in motion. In this case, since the crate is to be held in place, we are dealing with static friction.

Secondly, when solving for the normal force, it is important to consider the components of the weight of the crate that act in the x and y directions. The weight of the crate can be broken down into components of Wsin(30°) in the y-direction and Wcos(30°) in the x-direction. The normal force will then be equal to the sum of these two component forces.

Next, when solving for the tension in the rope, it is important to consider the forces acting on the crate in the y-direction. These forces include the weight of the crate and the tension in the rope, which must be equal and opposite in order for the crate to be held in place.

Finally, to find the maximum weight that can be used to hold the crate in place, we need to consider the maximum value of static friction, which is given by μsFn. This value must be greater than or equal to the force of gravity acting on the crate in the x-direction. This will give us the maximum weight that can be used to hold the crate in place.

In summary, to solve this problem, we need to consider the components of the weight of the crate, the forces acting on the crate in the y-direction, and the maximum value of static friction. Your approach of using the equations Fs = μsFn and F = ma is a good start, but it is important to consider all the forces and components involved in order to arrive at the correct answer. Keep up the good work!
 

FAQ: Frictional Forces Physics 1 Problem

What is frictional force in physics?

Frictional force is the force that opposes the motion of an object when it comes into contact with another object or surface. It is caused by microscopic bumps and irregularities on the surfaces of objects, which create resistance when they rub against each other.

How is frictional force calculated?

Frictional force can be calculated using the formula F = μN, where F is the frictional force, μ is the coefficient of friction, and N is the normal force. The coefficient of friction is a constant value that depends on the materials and surfaces in contact, while the normal force is the force perpendicular to the surface of contact.

What factors affect the magnitude of frictional force?

The magnitude of frictional force is affected by the coefficient of friction, the normal force, and the roughness of the surfaces in contact. A higher coefficient of friction or normal force will result in a greater frictional force, while smoother surfaces will have a lower frictional force.

How does frictional force affect an object's motion?

Frictional force acts in the opposite direction of an object's motion, so it can either slow down or stop the object's motion. It can also cause an object to change direction or prevent it from moving altogether.

What are some real-life examples of frictional force?

Some common examples of frictional force include the friction between a car's tires and the road, the friction between the sole of a shoe and the ground, and the friction between a pencil and a piece of paper when writing. Frictional force is also present in activities such as rubbing your hands together to create heat and using sandpaper to smooth out a rough surface.

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