In the figure below, the hanging object has a mass of m1 = 0.460 kg; the sliding
ID: 3280946 • Letter: I
Question
In the figure below, the hanging object has a mass of m1 = 0.460 kg; the sliding block has a mass of m2 = 0.830 kg; and the pulley is a hollow cylinder with a mass of M = 0.350 kg, an inner radius of R1 = 0.020 0 m, and an outer radius of R2 = 0.030 0 m. Assume the mass of the spokes is negligible. The coefficient of kinetic friction between the block and the horizontal surface is k = 0.250. The pulley turns without friction on its axle. The light cord does not stretch and does not slip on the pulley. The block has a velocity of vi = 0.820 m/s toward the pulley when it passes a reference point on the table.
(a) Use energy methods to predict its speed after it has moved to a second point, 0.700 m away? m/s
(b) Find the angular speed of the pulley at the same moment. rad/s
Explanation / Answer
Here ,
vi = 0.82 m/s
let the acceleration of the masses is a
Using second law of motion
a = net force/total effective mass
a = (0.460 * 9.8 - 0.250 * 0.830 * 9.8)/(0.460 + 0.830 + 0.50 * 0.350 * (0.020^2 + 0.030^2)/.030^2)
a = 1.604 m/s^2
a) Now, for the final speed vf
vf^2 - 0.82^2 = 2 * 9.8 * 0.70
vf = 3.79 m/s
the final speed is 3.79 m/s
b)
angular speed = final speed/outer radius
angular speed = 3.79/0.030 rad/s
angular speed = 126 rad/s
the final angular speed is 126 rad/s