A ball of mass M = 17 kg is suspended from a vertical inextensible string of len

Question

A ball of mass M = 17 kg is suspended from a vertical inextensible string of length l = 1.5 m. A bullet of mass m = M/2 traveling with a horizontal velocity v = 9sqrt(g*L) collides with the ball and gets stuck inside. As a result of the impact the ball moves in a vertical circle of radius L. Assume that the string remains taut throughout the motion. What is the velocity of the ball-bullet system at the highest point of the trajectory (Answer in units of m/s)? Also, what is the tension in the string at this point (Answer in units of N)? (g=9.8m/s^2)

Explanation / Answer

The forces acting on the block on the frictionless table are: Gravity, Tension, and the normal force The forces acting on the block on the string are: Gravity and tension Therefore the magnitude of the net external force is equal to F = 4.41097 kg * 9.8m/s^2 The magnitude of acceleration of the two masses is: (tension forces cancel as they are equal) m2*g = M*a m2*g = (m1+m2)*a a = m2*g/(m1+m2) where m2 = 4.41097kg, m1 = 2.45241kg, and g = 9.8m/s^2 To solve for the tension force, T. Use only one of the blocks, block 2 for example. T-F = m2*a T = m2*a + F

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