Help me start this one off?

Question

A 36kg box slides down a 29º ramp with an acceleration of 1.34 m/s^2

How do i find the coefficient of the kinetic friction between the box and the ramp??

friction must be considered

Answer 1

The force of friction is given by:

F(friction) = µN

Where
µ = coefficient of kinetic friction
N = normal force (= mg*cosΘ)

Find the net force on the box in the direction parallel to the ramp:

F(net) = F(g,parallel) - F(friction)
= mg*sinΘ - µmg*cosΘ

Newton's 2nd law tells us this is equal to the box's mass times its acceleration:

mg*sinΘ - µmg*cosΘ = ma

Solve for µ:
µmg*cosΘ = mg*sinΘ - ma
µg*cosΘ = g*sinΘ - a
µ = (g*sinΘ - a) / (g*cosΘ)
= 0.398

Answer 2

I am going straight to the solution a I am not that good at explainng things in words.

W = weight of the body sliding = mass(m) * gravitational force(9.81m/s)

a = acceleration of the body sliding
U = coefficient of friction

mgsin29 - U(mgcos29) = m * a
gsin29 - U(gcos29) = a

putting g=9.81m/s and a= 1.34m/s^2 as given

9.81sin29 - U (9.81cos29) = 1.34
U = (9.81sin29 - 1.34) / (9.81cos29)

Solve this and it will give you the answer for the coefficient of friction between the ramp and the box. Wile calculating make sure you get the brackets right.

Answer 3

Easy. On a frictionless ramp at 29 degrees, the acceleration would be

9.81 * sin 29

Instead, on this ramp, it is a mere 1.34.

The amount of acceleration lost to friction is

9.81 * sin 29 - 1.34

Since the forces at work are proportional to the accelerations involved, the coefficient of friction is

(9.81 * sin 29 - 1.34) / (9.81 * sin 29)

You don't have to know the mass of the sliding object.