Kinetic friction of box down a ramp

[runner1738]

A box slides down a ramp inclined at 41 degrees horizonontal with an acceleration of 1.4 m/s^2. The acceleration of gravity is 9.8 m/s^2. Determine the coefficient of kinetic friction between the box and the ramp.

no ideas need any advice

 

[xanthym]

A box slides down a ramp inclined at 41 degrees horizonontal with an acceleration of 1.4 m/s^2. The acceleration of gravity is 9.8 m/s^2. Determine the coefficient of kinetic friction between the box and the ramp.

no ideas need any advice

{Net Force On Box Parallel To Ramp} = {Gravity Parallel Component} - {Friction} =
= m*g*sin(41 deg) - K*m*g*cos(41 deg)
= m*g*{sin(41 deg) - K*cos(41 deg)}
= m*a

a = g*{sin(41 deg) - K*cos(41 deg)}
(1.4) = (9.8){(0.6561) - K*(0.7547)}
K = {(1.4/9.8) - 0.6561}/(-0.7547)
K = (0.6801)


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[thepatientmental]

The coefficient of kinetic friction can be determined by using the formula Fk = μkN, where Fk is the force of kinetic friction, μk is the coefficient of kinetic friction, and N is the normal force. In this case, the normal force is equal to the weight of the box, which can be calculated as mg, where m is the mass of the box and g is the acceleration due to gravity.

Using the given information, we can calculate the normal force as:

N = mg = (m)(9.8) = 9.8m

Next, we can calculate the force of kinetic friction using Newton's second law, F = ma, where F is the net force acting on the box and a is the acceleration. In this case, the net force is the force of kinetic friction, so we can rewrite the equation as Fk = ma. Substituting the values, we get:

Fk = (m)(a) = (m)(1.4) = 1.4m

Now, we can equate the two equations for Fk and solve for μk:

Fk = μkN

1.4m = μk(9.8m)

μk = 1.4/9.8 = 0.1429

Therefore, the coefficient of kinetic friction between the box and the ramp is approximately 0.1429. This means that the force of kinetic friction is about 14.29% of the normal force, which is causing the box to slow down as it slides down the ramp.