Answered: A 12.0-g wad of sticky clay is hurled…

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 9OQ

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Question

A 12.0-g wad of sticky clay is hurled horizontally at a 100-g wooden block initially at rest on a horizontal surface.

The clay sticks to the block. After impact, the block slides 7.50 m before coming to rest. If the coefficient of friction between the block and the surface is 0.650, what was the speed of the clay immediately before impact?

Expert Solution

Step 1

Scenario - Sticky clay is thrown towards a block such that after hitting it sticks to block. It then moves along with block till friction dissipates their motion.

Given :

Sticky class mass $\to m = 12.0 g = 0.012 k g$

Block mass $\to M = 100 g = 0.1 k g$

Block's initial velocity $\to u_{b l o c k} = 0 m / s$

Sliding distance $\to s = 7.50 m$

Friction co-efficient $\to μ = 0.650$

Step 2

By momentum conservation,

$\to m u_{b a l l} + M u_{b l o c k} = (M + m) v \Rightarrow m u_{b a l l} + M \times 0 = (M + m) v \Rightarrow v = \frac{m u_{b a l l}}{M + m}$

Putting all values,

$\Rightarrow v = \frac{0.012 u_{b a l l}}{0.1 + 0.012} \Rightarrow v = 0.107 u_{b a l l} (1)$

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