Force given mass, velocity and fricton

In summary: The initial velocity is 4 m/s, the acceleration is 1.96 m/s2, and the final velocity is 0 m/s. Plugging these values into the formula x = x0 + v0t + (1/2)at^2, you can find the distance the box travels before coming to rest, which is 4.08 meters. In summary, a 2 kg box is given a brief push and slides across the floor with an initial speed of 4 m/s. The coefficient of friction is 0.20. Using the equations for net force and friction, the net force is found to be 3.92 N. The box's acceleration is calculated to be 1.96 m
  • #1
Leopard_
2
0

Homework Statement


A 2 kg box is given a brief push so that it slides across the floor, but the applied force is only applied for an instant. The coefficient of friction is 0.20 and the initial speed of the box is 4 m/s.
Find acceleration of the box after the push
Find how far the box goes before coming to rest.

Homework Equations


Net force= mass*accel
Friction=u*normal

The Attempt at a Solution


I created an FBD, found the weight is 19.6N(9.8*2), and because it is being pushed horizontally, the Normal force is also 19.6 N. With the normal force I can find the force of friction. F=un, which means F=.2(19.6), and F=3.92 N. This leaves me missing the force I would need to calculate the Net f and find the accleration. I could only get this far, as I do not know how to find a force with only the velocity, mass, and friction.
 
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  • #2
Hello. Welcome to PF!
Leopard_ said:
Find acceleration of the box after the push
The push was only used to give the object an initial speed of 4 m/s. After that, the pushing force is zero.
 
  • #3
Oh, I suppose it was easier then I thought! Thank you!
 
  • #4
So, the box's acceleration of the box is slowing down by 9.81 m/s^2? Because it's initial speed is 4 m/s and there are not other forces acting on it?
 
  • #5
vr0nvr0n said:
So, the box's acceleration of the box is slowing down by 9.81 m/s^2? Because it's initial speed is 4 m/s and there are not other forces acting on it?
No, the box is not decelerating at 9.8 m/s2. You need to find the net force acting on the box and use Newton's second law of motion to find the acceleration.
 
  • #6
TSny said:
No, the box is not decelerating at 9.8 m/s2. You need to find the net force acting on the box and use Newton's second law of motion to find the acceleration.
Thank you. I got 1.96 m/s2 by dividing the Net Force by the mass. The Net Force, because this is all on a horizontal plane is the normal force multiplied by the coefficient of friction (3.92 N).

What formula would I need to use to find how far the box goes?

Thank you for your help.
 
  • #7
vr0nvr0n said:
Thank you. I got 1.96 m/s2 by dividing the Net Force by the mass. The Net Force, because this is all on a horizontal plane is the normal force multiplied by the coefficient of friction (3.92 N).
Yes.

What formula would I need to use to find how far the box goes?
You can use the standard kinematic formulas for constant acceleration.
 

1. What is force in terms of mass, velocity, and friction?

Force is a physical quantity that describes the amount of energy needed to change the motion of an object. It is directly related to the mass and velocity of an object, and is also affected by the presence of friction. In simpler terms, force can be thought of as a push or pull that causes an object to accelerate.

2. How does mass affect force?

Mass is a measure of an object's resistance to changes in motion. The greater the mass of an object, the more force is needed to accelerate it. This means that a heavier object will require more force to move at the same speed as a lighter object.

3. How does velocity affect force?

Velocity is a measure of an object's speed and direction. The greater the velocity of an object, the more force is needed to change its motion. This means that an object moving at a faster speed will require more force to be stopped or redirected than an object moving at a slower speed.

4. How does friction affect force?

Friction is a force that acts in the opposite direction of an object's motion, and it is caused by the interaction between two surfaces. When there is friction present, more force is needed to overcome it and maintain the object's motion. This means that friction can decrease an object's velocity and increase the amount of force needed to move it.

5. How can we calculate force given mass, velocity, and friction?

The equation for calculating force is F = ma, where F represents force, m represents mass, and a represents acceleration. In the case of an object experiencing friction, the equation becomes F = ma + μmg, where μ is the coefficient of friction and g is the acceleration due to gravity. By plugging in the values for mass, velocity, and friction, we can solve for the force acting on an object.

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