III) A 4-kg block resting on a incline is attached to a second block of mass m by a cord that passes over a smooth peg, as shown in the figure below. The coefficient of static friction between the block and the incline is 0.4. (a) Find the range of possible values for m for which the system will be in static equilibrium. (b) If m=1 kg, the system will be in static equilibrium. What is the frictional force on the 4-kg block in this case?

a) Case 1 (where static friction must act UP the incline to keep the system stationary)

[eq1]

[eq2]

T-mg=0 [eq3]

[eq2]+[eq3] [eq4]

[eq1]

For static friction to exist, we must have

b) Case 2 (where static friction must act DOWN the incline to keep the system stationary)

[eq5]

[eq6]

T-mg=0 [eq7]

[eq6]+[eq7] [eq8]

[eq5]

For static friction to exist, we must have

b) [eq4]

IV) A small block of mass m slides without friction along the loop-the-loop track as shown in the figure below. The block starts from point P a distance h above the bottom of the loop. What is the least value of h for which the block will reach the top of the loop without leaving the track? To solve this problem, you need to use the information given in class concerning the loop-the-loop.

a)

Block is barely on track when normal force equals zero.