a loading ramp problem?

Question

A box of textbooks of mass 24.4 kg rests on a loading ramp that makes an angle \alpha with the horizontal. The coefficient of kinetic friction is 0.270 and the coefficient of static friction is 0.330 .

As the angle \alpha is increased, find the minimum angle at which the box starts to slip.

At this angle, find the acceleration once the box has begun to move.
Take the free fall acceleration to be g = 9.80 m/s^2.

At this angle, how fast will the box be moving after it has slid a distance 5.50 m along the loading ramp?
Take the free fall acceleration to be g = 9.80 m/s^2.

Answer 1

The parallel component force on the block must overcome static friction to get moving. The force component is m*g*sin(alpha). The static friction is the coeff of friction times the perpendicular component of force, which is ks*m*g*cos(alpha). So the block begins to move when

m*g*sin(alpha) = ks*m*g*cos(alpha); tan(alpha) = ks

Once the static friction is overcome, the force moving the block is the parallel component of weight minus the friction, or

F = m*g*sin(alpha) - k*m*g*cos(alpha)

The block's acceleration is then a = F/m

The distance the block moves under constant acceleration a is s=.5*a*t^2; the velocity is given by v = a*t. Find t from the distance you were given and plug it into the formula for v.

Answer 2

http://en.wikipedia.org/wiki/Coefficient_of_friction