Finding F required pushing a box at angle (theta) for constant v

So the final equation should be:F = (Uk * (mg + Fsin(theta))) / cos(theta)In summary, to keep the crate moving at a constant velocity, a force F, with a magnitude of (Uk * (mg + Fsin(theta))) / cos(theta), must be applied at an angle of theta below the horizontal.
  • #1
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Homework Statement



a crate with mass m rests on a horizontal floor. a woman pushes down at an angle of theta below the horizontalon the frace with a force F, the coefficient of kinetic friction is Uk.
a) what magnitude of force F is required to keep the crate moving at a constant velocity?

Homework Equations



Ff(frictional force)=UkFn

Constant velocity which means Fnet=0

The Attempt at a Solution



since Fnet is 0 you can set horizontal force = to frictional force

Ff=Fsin(theta)
Uk(mg + Fcos(theta))=Fsin(theta)
(Uk(mg+ Fcos(theta))/sin theta = F

This is apparently not right and i can't thing of what else to do -_- help would be very much appreciated as well as an easier way of approaching problems with only symbols.
thanks!
 
Last edited:
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  • #2
You are very close, but I think you mixed up the components of F. I think your cos and sin should be switched.
 

1. How does the angle affect the force required to push the box?

The angle at which the box is pushed affects the direction of the force applied, but not the magnitude of the force. The force required to push the box at a constant velocity will be the same regardless of the angle, as long as the surface of the box is flat and the force is applied directly perpendicular to it.

2. Why is the velocity constant in this scenario?

In this scenario, the velocity is constant because the force applied to the box is balanced by the frictional force of the surface it is being pushed on. As long as the net force on the box is zero, it will continue to move at a constant speed.

3. What other factors can affect the force required to push the box?

The force required to push the box may also be affected by the weight of the box, the coefficient of friction between the box and the surface it is being pushed on, and any external forces acting on the box (such as wind or inclines).

4. How can the force required be calculated for a given angle?

The force required to push the box at a given angle can be calculated using trigonometry. The force can be broken down into its x and y components, with the x component being the force applied parallel to the surface and the y component being the force applied perpendicular to the surface. The total force required can then be calculated using the Pythagorean theorem.

5. Does the force required change if the box is pushed on a different surface?

Yes, the force required to push the box may change if the surface it is being pushed on has a different coefficient of friction. A surface with a higher coefficient of friction will require more force to push the box at a constant velocity, while a surface with a lower coefficient of friction will require less force. The angle at which the box is pushed may also affect the force required on different surfaces.

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