Unbalanced force - at rest

In summary, the box will be pushed to the top of the ramp in 4.22 seconds if a constant force of 19.43 newtons is applied parallel to the slope of the ramp.
  • #1
BOAS
552
19
Hi,

i'm stuck on a mechanics problem where the initial conditions are a mass at rest on an inclined plane, but the forces are seemingly unbalanced.

1. Homework Statement

A 5.17 kg box sits at rest at the bottom of a ramp that is 8.56 m long and that is inclined
at 40.0◦ above the horizontal. The coefficient of kinetic friction is 0.40, and the coefficient
of static friction is 0.50.
What constant force F, applied parallel to the surface of the ramp, is required to push the
box to the top of the ramp in a time of 4.22 s ?

Homework Equations

The Attempt at a Solution



I have drawn a freebody diagram with the weight of the box acting straight down. perpendicular to the slope, we have the component $$mg \cos(\theta)$$ and the normal force being $$-mg \cos(\theta)$$. parallel to the slope, a component of the weight acts down the the slope $$mg \sin(\theta)$$ and the force of static friction opposes this motion.

Static friction $$f_{s} \leq \mu_{s} n$$ where $$n = -mg \cos(\theta) = -19.43 N$$

This is the max force that can be applied parallel to the slope without the box beginning to move, but the component of weight acting down the slope is greater than this, so why is the box not moving?

Was I supposed to consider "at the bottom of the slope" to mean the normal force = weight?
 
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  • #2
Maybe it is just being held there before the force parallel to incline is applied. It is just a pre-condition to start the problem.
 
  • #3
It seems to me that I don't need this information to solve the problem.

The applied force is parallel to the slope, so kinetic friction remains constant. Using the equations of kinematics, I can determine the acceleration required to cover the distance in that time. Using Newton's second law, I can determine what the net force must be, and therefore the applied force is equal to the difference between the kinetic friction and resultant force.
 
  • #4
BOAS said:
It seems to me that I don't need this information to solve the problem.
You need to know that it starts at the bottom and that it starts from rest. No hidden meaning beyond that.
 
  • #5
Doc Al said:
You need to know that it starts at the bottom and that it starts from rest. No hidden meaning beyond that.
Thanks
 

1. What is an unbalanced force?

An unbalanced force is a force that causes a change in an object's motion. It is a force that is not opposed by an equal and opposite force, resulting in a net force acting on the object.

2. How does an unbalanced force affect an object at rest?

An object at rest will remain at rest unless acted upon by an unbalanced force. If an unbalanced force is applied to an object at rest, it will cause the object to move in the direction of the force.

3. What are some examples of unbalanced forces?

Examples of unbalanced forces include pushing or pulling an object, gravity pulling objects towards the Earth, and friction between two surfaces.

4. How do you calculate the net force of an object with unbalanced forces?

To calculate the net force of an object with unbalanced forces, you must add up all of the individual forces acting on the object. The direction of the net force will be in the same direction as the larger force.

5. How can you achieve equilibrium with unbalanced forces?

Equilibrium occurs when an object has a net force of zero, meaning that the forces acting on the object are balanced. To achieve this with unbalanced forces, the magnitude and direction of the forces must be equal and opposite.

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