Find Friction Force of Box with Mass of 135 kg at 35° Angle

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In summary, the worker applies a force of 2030 N at an angle of 215° to a box with a mass of 135 kg, causing it to move horizontally to the left at a constant velocity. The friction force on the horizontal plane is approximately 1663 N, as the forces are balanced and the net force is 0.
  • #1
DaDoctor
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The worker pushes downward and to the left on the box at an angle of 35°. The box has a mass of 135 kg. The box moves horizontally across the floor to the left at a constant velocity. The force applied by the worker is 2030 N∠215°. What is the value of the friction force?Fgravity · sin35° = Fgravityx
Ffriction + Fgravityx = m · a
f = μ · Fssin35° =
Fgravity · sin35° = Fgravityx
m · g · sin35° = Fgravityx
(135 kg)(9.81) sin35° = Fgravityx
759.6 N = Fgravityx

Ffriction + (759.6 N) = (135 kg)(0 m/s2)
Ffriction - 759.6 N = 0 N
Ffriction = 759.6 N

I know that this isn't correct, because my study guide is multiple choice. My options are:
a. 1164 N
b. 1324 N
c. 1663 N
d. 2489 N

I'm really not sure what I'm missing or if I am going the wrong way with finding the value of the friction force. My guess is that c. 1663 N is correct, but that is only a guess. I'd like to be able to prove which answer it is. Thank you for any help!
 
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  • #2
Your guess is right. Your calculations are off quite a bit. What can you conclude about the friction force since the box is moving to the left at a constant velocity?
 
  • #3
Probably that it is about equal to the Horizontal force, and that the Net Force is 0
 
  • #4
Student100 said:
Your guess is right. Your calculations are off quite a bit. What can you conclude about the friction force since the box is moving to the left at a constant velocity?

Probably that it is about equal to the Horizontal force, and that the Net Force is 0
 
  • #5
So the forces are balanced right? So to calculate the frictional force on the horizontal plane why are you using sin and fg? What should you do instead?
 
  • #6
DaDoctor said:
Probably that it is about equal to the Horizontal force, and that the Net Force is 0
Exactly, so what is the Ff in the horizontal direction?
 
  • #7
Student100 said:
Exactly, so what is the Ff in the horizontal direction?
... about 1663 Newtons of force since it is a total of 2030N at a 215 degree angle.
 
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DaDoctor said:
... about 1663 Newtons of force since it is a total of 2030N at a 215 degree angle.
Yep. =)
 
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  • #9
Student100 said:
Yep. =)
Awesome! Thanks a lot!
 

1. How do you calculate the friction force of a box with a mass of 135 kg at a 35° angle?

The formula for calculating friction force is Ff = μN, where Ff is the friction force, μ is the coefficient of friction, and N is the normal force. To find the normal force, we need to resolve the force of gravity into its components. The normal force is equal to the component of the force of gravity perpendicular to the surface, which can be calculated as N = mgcosθ. Plugging in the given values, we get Ff = μ*135*9.8*cos35°.

2. What is the coefficient of friction for this scenario?

The coefficient of friction is a dimensionless quantity that represents the amount of friction between two surfaces. It depends on the nature of the surfaces in contact and the roughness of their surfaces. Without knowing the specific materials and conditions, it is impossible to determine the coefficient of friction. However, it can be measured experimentally.

3. How does the angle affect the friction force?

The angle of the incline affects the normal force, which in turn affects the friction force. As the angle increases, the normal force decreases, resulting in a smaller friction force. This is because a greater portion of the force of gravity is acting parallel to the surface, reducing the normal force component.

4. Is the friction force always acting against motion?

No, the direction of friction force depends on the direction of motion or the applied force. If the box is moving down the incline, the friction force will act in the opposite direction to slow it down. However, if an external force is applied to move the box up the incline, the friction force will act in the same direction to oppose that force.

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

No, the friction force can never be greater than the force of gravity. The maximum possible friction force is given by Ff = μN, and the normal force is always less than or equal to the force of gravity. Therefore, the maximum friction force is always less than or equal to the force of gravity.

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