A simple pendulum consisting of a 5.0kg mass and a rod oflength 1.6m (rod has no

Question

A simple pendulum consisting of a 5.0kg mass and a rod oflength 1.6m (rod has no mass). The pendulum is released fromrest at a 20 deg angle below the horizontal. When thependulum is vertically straight down, it collides with a 2.0kg massthat is traveling straight horizontally to the right with avelocity of 2.00 m/s. After the collision, the 2.0kg masstravels .425m to the left before coming to a stop. If thecoefficient of kinetic friction between the 2.0kg mass andhorizontal surface is .300, find the following: a) the maximum vertical height of the 5.0kg mass and thecorresponding angle the rod makes with the vertical after thecollision between the masses. b) the work done by gravity on the5.0kg mass as it travels from the collision point to its maximumheight. Any help is appreciated, thank you

Explanation / Answer

M = 5.0 kg, L = 1.6 m, = 20o,m = 2.0 kg, d =0.425 m, = 0.300, choose right as positive direction. before collision: velocity of M = V, velocity of m = v = 2.00m/s. after collision: velocity of M = V', velocity of m = v' use MV2/2 = MgL(1 - sin) and get V =-[2gL(1 - sin)] = -4.542 m/s use mv'2/2 = mgd and get v' = -(2gd)= -1.581 m/s use mv + MV = mv' + MV' and get V' = V + m(v - v')/M = -3.110m/s a) maximum height = h MV'2/2 = Mgh h = V'2/(2g) = 0.493 m angle = ' where h = L(1 - cos'), so ' =cos-1(1 - h/L) = 46.2o b) work done = -Mgh = -24.2 J

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