Calculating Mass from Applied Force and Coefficient of Kinetic Friction

In summary, the crate has an applied force of 524N at 12 degrees below horizontal and moves with constant velocity. The coefficient of kinetic friction is 0.15. To find the mass of the crate, a free body diagram must be used to determine the normal force, which is equal to the frictional force divided by the coefficient of kinetic friction. The weight of the crate must also be taken into account by subtracting the vertical component of the applied force from the normal force. Finally, the mass can be calculated by dividing the weight by the acceleration due to gravity. The mass of the crate is approximately 340kg.
  • #1
yoshi6
63
0

Homework Statement



A crate on a floor has an applied force (12 degrees below horizontal) of 524N. The crate moves with constant velocity. The coefficient of kinetic friction is 0.15. What is the mass of the crate?

Homework Equations



Fk=uk*Fn, Fn= m * g

The Attempt at a Solution



OKay so this is what I did. Apparently it is not right, my teacher said it is 80% right. Can someone please tell me what I am doing wrong. As soon as possible would be really helpful. Thanks


Fn= 524cos12
= 512.5493428

m= ukFn/ g
= (0.15)(512.5493428N)/(9.81m/s^2)
= 7.8kg
 
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  • #2
Can someone please help me
 
  • #3
You are forgetting to include the weight of the crate in your calculations. Draw a free body diagram.
 
  • #4
but the question is asking for the weight...is it not?
 
  • #5
It is asking for the mass. In your work you have the normal force based on the applied force only, you must also include the weight of the crate, that is acting downwards.
 
  • #6
So that would be the Fy value? Which is 524Sin12= 108.945726 then I add this value to the Fx value? So,

F(normal force) = 108.945726+512.5493428 =621.5 N ?
 
  • #7
No, you are just using the same force for everything, that makes no sense.

1. Do you know what the normal force represents?

2. You need to identify ALL of the forces acting on the crate. You have the normal force, the applied force (which you must resolve into components, like you've done), you have friction, and you have the weight. You need to sum up the forces in both directions (horizontal and vertical) to get two equations. The "vertical" equation will give you an expression for the normal force. You can then use this expression in your "horizontal" equation so you can solve for the mass of the crate.

3. Draw a diagram with all the forces. There should be examples of this in your textbook.
 
  • #8
I do have a free body diagram that my teacher said is correct. I know normal force =mg. But if I don't have the mass how can I find the normal force? I know I have to substract the frictional force but again I need the mass to figure this out. Right?
 
  • #9
I don't know. I don't understand. Thanks anyway.
 
  • #10
The normal force does not equal just mg, though. This is because you have the applied force there as well. You need to add up ALL of the forces in the vertical direction.
So N - mg - Fy = 0
where Fy is the vertical component of the 524 N force.

Does that help?
 
  • #11
I think so...524-109=mg?
 
  • #12
oh! F(normal force) = mg = 524-109
 
  • #13
I think so...524-109=mg?

No.

You don't know N directly. Maybe my notation is confusing you. When I wrote "N" in that equation, I meant Fn [F(normal force)]. Is that what you are used to? Fn is not 524 Newtons. 524 Newtons is the applied force. They are not the same thing.

Looking at your free body diagram, you should have Fn upwards, Fy downwards, and mg downwards. You are correct that Fy = 109 Newtons.

You want to express this as Fn = Fy + mg for now.

The second thing you need to do is look at the forces in the horizontal direction to get another equation. So what forces do you have there, based on your free body diagram? Add them up, like we did for the vertical direction.
 
  • #14
Ok this is what I have come up with:::

F(friction) = 524cos12= 513N

so now I have,

F(friction) =(uk)(Fn)

Fn= F(friction)/ (uk)
= 513/0.15
=3420

Weight= 3420- 524sin12
=3308

So,

Weight = mg

m=weight/g
=3308/9.81
=340kg

? I hope...
 
  • #15
Can anyone tell me if this is right?
 

What is kinetic friction?

Kinetic friction is a type of friction that occurs between two objects when they are in motion relative to each other. It is caused by the microscopic irregularities on the surface of the objects that come in contact with each other.

How is kinetic friction different from static friction?

Kinetic friction occurs when two objects are already in motion, while static friction occurs when two objects are at rest and trying to be set in motion. Kinetic friction is typically smaller than static friction.

What factors affect the magnitude of kinetic friction?

The magnitude of kinetic friction depends on the nature of the surfaces in contact, the force pressing the objects together, and the speed of the objects in motion. It is also affected by factors such as temperature, surface area, and the presence of lubricants.

How is kinetic friction measured and expressed?

Kinetic friction is measured in units of force, such as newtons or pounds, and is typically represented by the symbol "Fk". It can be calculated by multiplying the coefficient of kinetic friction (μk) by the normal force (N) exerted on the object.

What are some real-life examples of kinetic friction?

Some examples of kinetic friction in everyday life include the movement of a car on the road, a person walking on the ground, or the movement of a pencil on paper. It is also present in activities like skiing, ice skating, and bowling.

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