physics help please...?

Question

a 75 kg box slides down a 25.0 degree ramp with an acceleration of 3.60 m/s^2. Find ,uk between the box and the ramp. What acceleration would a 175kg box have on this ramp?

Answer 1

Let m = 75 kg box mass, theta = 25 degree incline, a = 3.6 m/sec^2, and g = 9.81 m/sec^2. f = ma = (mg sin(theta) - kmg cos(theta)) = mg(sin(theta) - k cos(theta)); where f is the net force acting along the ramp to give the box acceleration, W = mg the weight of the box, and k is the coefficient of friction.

Solve for k in ma = mg(sin(theta) - k cos(theta)); so that a/g = sin(theta) - k cos(theta) and a/g - sin(theta) = - k cos(theta). Thus k = [sin(theta) - a/g]/cos(theta); where everything is known on the RHS, so you can do the math.

Notice that k does not depend on the mass of the box. So this result would be the same no matter how big or small the box is. And that's the physics lesson this problem is all about.

Answer 2

you determine the acceleration down the ramp by using newtons's second law:

Sum forces down ramp = ma

Sum forces = component of gravity down-friction
= mg sin(theta)-uk mg cos(theta)=ma

notice that the m's cancel out, leaving:

a=g(sin(theta)-uk cos(theta)

In other words, acceleration depends only on gravity, the angle, and the coefficient of friction and not on mass. So, the answer is: the heavier box will have the same acceleration down the plane.

Sorry, I didnt see the question for finding uk. Go back to the equation above:

a=g(sin(theta)-ukcos(theta)) and substitute values:

3.6m/s^2 = 9.8m/s^2(0.4226-0.9063uk))

Solving for uk gives 0.061

Answer 3

1 meter square