Problem #2 (30 pts) A piece of clay with a mass of 5 kg is attached to a string

Question

Problem #2 (30 pts) A piece of clay with a mass of 5 kg is attached to a string that has a length of3 m. The other end of the string is atached to the ceiling so the piece of clay can swing freely like a pendulum. At the exact bottom of the pendulum, block and mass together then continues to act like a pendulum with the higher combined mas problem, neglect any effects due to air resistance there is a small wooden block. When released, the piece of clay strikes and sticks to the block. The s. For this (a) (12 pts) If the piece of clay was released at a height of0.5 m with an initial speed of 1.2 m/s perpendicular to the string direction (to keep the string tight), what is the speed of the piece of clay immediately before it strikes the block? (b) (12 pts) If the speed of the block and clay is 2 m/s after the collision, what is the mass of the block? If you did not find the speed from part a) and it is needed, assume you know the quantity and solve algebraically (c) (6 pts) What is the maximum height reached by the connected masses as they stop after the collision?

Explanation / Answer

Given mass os clay mc = 5 kg

mass of block mb = ?

a) height h = 0.5 m

initial speed u = 1.2 m/s

let speed of the clay before collision is 'v'

from conservation of energy we have

mc * g * h = (1/2 * mc * v^2) - (1/2 * mc * u^2)

5 * 9.8 * 0.5 = (1/2 * 5 * v^2) - (1/2 * 5 * 1.2^2)

v = 3.35 m/s

b)

from conservation of momentum

momentum before collision = momentum after collision

mc * v = (mc + mb) * v1

5 * 3.35 = (5 + mb) * 2

mb = 3.375 kg

c)

from conservation energy again

1/2 * (mc + mb) * v1^2 = (mc + mb) * g * h

h = v1^2 / 2g

h = 2^2 / (2*9.8)

h = 0.2 m

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