A ball of putty of mass M is hooked onto a massless rope of Problems 6-8 length

Question

A ball of putty of mass M is hooked onto a massless rope of Problems 6-8 length The ball and rope are released from a horizontal position as shown. At the instant that the rope is vertical the ball collides with an identical stationary ball and sticks. At this point the two balls are released from the hook and slide without friction until they are stopped by a spring of constant MM 6. Find an expression for the tension in the rope just before the balls touch. 7. Find an expression for the speed of the balls just after they stick together.

Explanation / Answer

6) at the bottom point of the verticle circular motion

T - mg = m*v^2/R

T - Mg = M*v^2/L

Tension is T = Mg + (M*V^2/L)

V = sqrt(2*g*L)

T = Mg + (M*2*g*L/L)

T = 3 *M*g

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7) Using law of conservation of momentum

M*v = (M+M)*Vf

Vf = M*sqrt(2*g*L)/(2M)= sqrt(gL/2)

8) Using law of conservation of energy

0.5*(M+M)*(gL/2) = 0.5*k*x^2

2*M*gL/2 = k*x^2

3*9.8*1.2 = k*0.06^2

k = 9800 N/m

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