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M1 900 M2 L Ax

M1 900 M2 L Ax

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Hi I need help with the following question

M1 A pendulum of length L and bob with mass M1 is released from rest at an angle = 90° from the 1. 900 %3D vertical. When the pendulum reaches the vertical position, the bob strikes an object of mass m2 that is resting on a frictionless table. At impact, the M2 pendulum string bob snaps as the two objects stick together and move as one. Derive expressions for each of the following in terms of M1, M2, L and g Ax а. Calculate the speed of M1 just before the collision with the object. b. Calculate the tension in the string just before the collision when it snaps at impact between M1 and M2 с. Calculate the speed of M1 and M2 just after the collision when they are stuck together. d. After impact, the pendulum string snaps and the two masses fall together off of the table. Calculate the horizontal distance Ax from the base of the table where the two masses hit the floor.
Transcribed Image Text:M1 A pendulum of length L and bob with mass M1 is released from rest at an angle = 90° from the 1. 900 %3D vertical. When the pendulum reaches the vertical position, the bob strikes an object of mass m2 that is resting on a frictionless table. At impact, the M2 pendulum string bob snaps as the two objects stick together and move as one. Derive expressions for each of the following in terms of M1, M2, L and g Ax а. Calculate the speed of M1 just before the collision with the object. b. Calculate the tension in the string just before the collision when it snaps at impact between M1 and M2 с. Calculate the speed of M1 and M2 just after the collision when they are stuck together. d. After impact, the pendulum string snaps and the two masses fall together off of the table. Calculate the horizontal distance Ax from the base of the table where the two masses hit the floor.
Expert Solution
Step 1

a) By using law of conservation of energy 

(K.E + P.E)initial = (K.E + P.E)final                                      ..... i)

the bob is release from rest i.e its velocity at that point is zero

and its potential energy P.E = m1gh = m1g(2L)

 

And at final position, just before the collision

potential energy P.E = m1gh = m1g(L)

having kinetic energy K.E = 12 m1v12

From equation i)

2m1gL = m1gL + 12 m1v1212 m1v12 = m1gLv1 = 2gL

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