Calculate the Force of a Certain Push

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In summary, to find the minimum force required to keep a 5kg book from sliding down a vertical wall at a 25 degree angle with a coefficient of static friction of .76, one must set up and solve equations using the force of gravity and the force of push in both the x and y directions. This will provide the necessary information to determine the minimum force needed to keep the book at rest.
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Darkstr958
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Homework Statement


A person exerts a force 25 degrees to the horizontal on a 5kg book resting against a vertical wall. If the coefficient of static friction is .76, what is the minimum force that the person must exert to keep the book from sliding down the wall.


Homework Equations


force of friction= coeffecient of static friction * normal force
fg=mg

The Attempt at a Solution


I know the net force must be zero for the book to be at rest, so all the forces have to cancel each other out. Also, the force of gravity is 49N. I also know you need to resolve the force of the push into its x and y components since its at a 25 degree angle. normal force should be opposite the force of the push along the x-axis, and the force of gravity should be opposite the force of friction plus the force of the push in the y direction, but I don't seem to have enough information to find out many of these values.
 
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  • #2
Welcome to PF!

Hi Darkstr958! Welcome to PF! :smile:

(have a mu: µ and a degree: º :wink:)
Darkstr958 said:
I know the net force must be zero for the book to be at rest, so all the forces have to cancel each other out … but I don't seem to have enough information to find out many of these values.

Call the force F.

You have two equations, one with F cos25º, and one with F sin25º. You also have friction = µsN, so you have two unknowns (F and N) and two equations. :smile:
 
  • #3


The minimum force that the person must exert to keep the book from sliding down the wall can be calculated by using the equation Fpush = Ffriction + Fgravitysin(θ), where Fpush is the force that the person exerts on the book, Ffriction is the force of friction, Fgravity is the force of gravity, and θ is the angle at which the force is applied (in this case, 25 degrees).

First, we need to find the normal force, which is equal to the force of gravity in this case since the book is at rest. So, Fnormal = Fgravity = 49N.

Next, we can calculate the force of friction using the equation Ffriction = μFnormal, where μ is the coefficient of static friction. So, Ffriction = 0.76 * 49N = 37.24N.

Now, we can plug these values into our original equation to solve for Fpush:

Fpush = 37.24N + 49N*sin(25)

Fpush = 37.24N + 20.52N

Fpush = 57.76N

Therefore, the minimum force that the person must exert to keep the book from sliding down the wall is 57.76N.
 

What is the formula for calculating force?

The formula for calculating force is F = m x a, where F represents force, m represents mass, and a represents acceleration.

What units are used to measure force?

The SI unit for force is the Newton (N). Other commonly used units include pound-force (lbf) and kilogram-force (kgf).

How do I calculate the force of a push on an object?

To calculate the force of a push on an object, you will need to know the mass of the object and the acceleration it experiences. Once you have those values, you can use the formula F = m x a to calculate the force.

What does a negative force value mean?

A negative force value indicates that the force is acting in the opposite direction of the chosen positive direction. It does not necessarily mean that the force is "weaker" or "less" than a positive force.

Can I use this formula to calculate any type of force?

Yes, this formula can be used to calculate any type of force as long as you have the necessary information (mass and acceleration) for the specific situation.

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