# Physics

A box, with a weight of mg = 25 N, is placed at the top of a ramp and released from rest. The ramp measures 4.40 meters horizontally and 3.50 meters vertically. The box accelerates down the incline, attaining a kinetic energy at the bottom of the ramp of 54.0 J. There is a force of kinetic friction acting on the box as it slides down the incline.

a) What is the coefficient of kinetic friction between the box and ramp? & please show work.

1. 👍 0
2. 👎 0
3. 👁 507
1. Equate the work done against friction to the mechanical (potential + kinetic) energy loss. That will allow you to solve for the friction coefficient, Uk.

The slope of the ramp is arctan 3.5/4.4 , which is 38.5 degrees.

The hypotenuse of the ramp is 5.622 m

Show your work for further assistance.

1. 👍 0
2. 👎 0
2. I know the work done is

W = ì X mgcosè X d

and W is Ui+ W= Kf which is 54-(25*3.3)=-33.5

so W = ì X mgcosè X d

and so ì= (W/(mgcosè X d))

and mg=25N so what is cosè? and i think d is the hypotenuse?

1. 👍 0
2. 👎 0
3. im sorry it should be cos theta for all of them

1. 👍 0
2. 👎 0
4. and the "i" looking thing is the coefficient of friction

1. 👍 0
2. 👎 0
5. It would be easier to do it the way Dr WLS suggested.
vertical distance down = 3.5 m
so potential energy lost = mgh=25*3.5 =87.5 Joules
It has Ke of 54 Joules at the bottom so lost (87.5-54) = 33.5 Joules to friction
Friction force * length of ramp = 33.5
length of ramp = sqrt(3.5^2+4.4^2) = 5.62 meters
so friction force = 33.5/5.62 = 5.96 Newtons
so
5.96 = mu*normal force
5.96 = mu * (25 cos slope)
cos slope = 4.4/5.62
so
mu = 5.96 *5.62/(4.4*25) = .238

1. 👍 0
2. 👎 0
6. Ohh I see! Thanks a lot!

1. 👍 0
2. 👎 0

## Similar Questions

1. ### physics

A large box of mass M is pulled across a horizontal, frictionless surface by a horizontal rope with tension T. A small box of mass m sits on top of the large box. The coefficients of static and kinetic friction between the two

2. ### Physics

A 20.0 kg box rests on a table. what is the weight of the box and the normal force acting on it? A 10.0 kg box is set on top of the 20.0kg box. Determine the normal force that the table exerts on the 20.0kg box and the normal

A box weighing 65.0 N rests on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end. Part a) Determine the force that the table exerts on the box if the weight hanging on the

A box of weight w=2.0 N accelerates down a rough plane that is inclined at an angle 30 degrees above the horizontal. The normal force acting on the box has a magnitude n= 1.7 N, the coefficient of kinetic friction between the box

1. ### CIVICS

The diagram below shows that the colonists formed some of their political views from historical documents.There are two sets of two boxes. The top box to the left says English Bill of rights. Then there is an arrow pointing to the

2. ### physics

The drawing shows box 1 resting on a table, with box 2 resting on top of box 1. A massless rope passes over a massless, frictionless pulley. One end of the rope is connected to box 2, and the other end is connected to box 3. The

3. ### Calculus

A box has rectangular sides, top and bottom. The volume of the box is 3 cubic meters. The height of the box is half the width of the base. Express the total surface area of the box in terms of the height of the box.

4. ### Physics

You drag a heavy box along a rough horixontal floor by a horizontal rope. Identify the reaction force to each ofthe follwing forces: A) the pull of the tope on the box. B) the friction force on the box C) the normal force on the

1. ### physics

The drawing shows a top view of a square box lying on a frictionless floor. Three forces, which are drawn to scale, act on the box. Consider an angular acceleration with respect to an axis through the center of the box

2. ### calculus

A closed cardboard box is made with a square top and bottom, and a square horizontal shelf inside that divides the interior in half. A total of 12 square meters of cardboard is used to make the top, sides, bottom, and shelf of the

3. ### Pre Cal 12

A 12cm by 8cm rectangular piece of metal is to be made into an open-top box by cutting a sqaure from corner and folding up the resulting flaps (sides). If the volume of the lidless box is 36 cm what are the integer dimensions of

4. ### physics

A 47 N box is pulled along a frictionless horizontal surface by a 25 N weight hanging from a cord on a frictionless pulley? What is the acceleration of the system (box and the weight)?