Determine the coefficient of kinetic friction between surface and block over the track length?

Question

A 302 kg block is released at height h = 4.4 m as shown. The track is frictionless except for a portion of length 6.6 m. The block travels down the track, hits a spring of force constant k = 1993 N/m, and compresses it 2.6 m from its equilibrium position before coming to rest momentarily.

The acceleration of gravity is 9.8 m/s^2.

Determine the coefficient of kinetic friction between surface and block over the 6.6 m track length.

Answer 1

Since you didn't include a diagram, I will make some assumptions. The solution will be expressed in terms of the angle th which is the angle subtended by the track and the horizontal plane.

The track is greater that 6.6 m in length. The angle th must be less than arcsin(4.4/6.6), or less than 41.8 degrees. I will also assume that the block encounters the spring in such a way that the total vertical displacement of the block is 4.4 m as if the block slides down the track and then travels horizontally when it encounters the spring.

I will use conservation of energy to solve.

The work done in the system includes:

Loss in potential energy due to vertical displacement

=m*g*h
=302*9.8*4.4
13022.24
The units are Joules

Loss due to friction
First, compute the Normal force, N

N=m*g*sin(th)
=302*9.81*sin(th)
=2960*sin(th)

The force of friction is N*u
where u is the coefficient of friction

and the work is N*u*d

in this case
2960*sin(th)*u*6.6
=19536*sin(th)*u

The increase in potential energy of the spring

=.5*k*x^2
=.5*1993*2.6*2.6
6736.34


setting up the conservation of energy

13022-19536*sin(th)*u-6736=0

sin(th)*u=(13022-6736)/19536

0.322

j

Answer 2

you've left out a crucial piece of advice -- the genuine the block drops from (h), and the slope of the song between B and C. the following, it really is a conservation of power question. PE - Friction loss = Spring power PE = mgh m = 10 kg Friction loss = F*d = d * Cf * mgh * cos theta d= 6 m cos theta = perspective of B to c ..... (If the song is flat, cos theta = a million) Spring power = a million/2 ok x^2 x = .3m Substituting in mgh - d * Cf * mgh * cos theta = a million/2 ok x^2 %. off the lacking variable and sparkling up