Part 1:
Problem 1:
Two blocks connected through a series of pulleys are originally at rest. Neglect the mass and any friction of the pulleys. Assume that the friction coefficients between block A and the surface are µs=0.25 and µk=0.20. Determine the following:
(a) The acceleration of each block
(b) The tension in the cable.
Problem 2:
A 450 gram tetherball A is moving along a circular horizontal path at a constant speed of 4 m/s.
Determine:
(a) The angle θ that the cord forms with pole BC
(b) The tension in the cord.
Problem 3:
A small 300 gram collar D can slide on the segment of the rod as shown. Knowing that α=40o and that the rod rotates about the vertical AC at a constant rate of 5 rad/s, determine the value of r for which the collar will not slide on the rod if the effect of friction between the rod and collar is neglected.
Part 2:
Problem 1:
The rod shown rotates about O in a horizontal plane. The motion of the 5 pound collar B is defined by r = 10/(t + 4) and θ = (2/Π)sin (Πt), where r is in feet, t is in seconds, and θ is in radians. Determine the radial and transverse components of the force exerted on the collar when (a) t=1s and (b) t=6s.
Problem 2:
A particle of mass m is projected from a point A with an initial velocity v0 perpendicular to line OA and moves under a central force F along a semicircular path of diameter OA. Observing that ?? = rocos(θ), show that the speed of the particle is v = vo/cos2θ . (hint: since the particle is moving under a central force, angular momentum is conserved between any two points on the curve. Additionally, you will want to make use of radial and transverse coordinates).
Problem 3:
Determine the mass of the earth knowing that the mean radius of the moon's orbit about the earth is 238,910 miles and that the moon requires 27.32 days to complete one full revolution about the earth.