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Name: A 0.5kg puck slides to the right with a speed of 1.0m/s on a frictionl
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Description: A 0.5kg puck slides to the right with a speed of 1.0m/s on a frictionless surface and collided with a rock of mass M which is at rest. After the collision, the 0.5kg puck recoils to the left with a speed of 0.5m/s and the rock with the mass M moves t

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter8: Momentum And Collisions

Section: Chapter Questions

Problem 5OQ: A 5-kg cart moving to the right with a speed of 6 m/s collides with a concrete wall and rebounds...

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A 0.5kg puck slides to the right with a speed of 1.0m/s on a frictionless surface and collided with a rock of mass M which is at rest. After the collision, the 0.5kg puck recoils to the left with a speed of 0.5m/s and the rock with the mass M moves to the right with a speed of 0.5m/s.
A.) Find M (to 4 significant figures)

B.) What type of collision is this? (Justify your answer)

Expert Solution

GIVEN:

Mass of the puck, $m = 0.5 k g$

Velocity of puck before collision, $v_{i} = 1.0 m / s$

Velocity of puck after collision, $v_{f} = 0.5 m / s$

Mass of the rock, $M$ = ?

Velocity of rock before collision, $V_{i} = 0$

Velocity of rock after collision, $V_{f} = 0.5 m / s$

(A) Find the mass of rock, $M$

(B) What type of collision is this?

SOLUTION PART-1:

(A) Find the mass of rock, $M$ :

For a collision, the momentum is always conserved, that is,

$T h e t o t a l m o m e n t u m b e f o r e c o l l i s i o n = T h e t o t a l m o m e n t u m a f t e r c o l l i s i o n$

That is,

$m v_{i} + M V_{i} = m v_{f} + M V_{f}$

Substituting the values for above equation,

$(0.5 k g) (1.0 m / s) + M (0) = (0.5 k g) (0.5 m / s) + M (0.5 m / s)$

$0.5 k g m / s = 0.25 k g m / s + M (0.5 m / s)$

Rearranging the equation for calculating the mass of rock, we have,

$M (0.5 m / s) = (0.5 - 0.25) k g m / s$

$M = \frac{0.25}{0.5} k g$

$M = 0.5 k g$

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