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Chapter 1: Q82P (page 269)

Two identical masses are released from rest in a smooth hemispherical bowl of radius R from the positions shown in Fig. P8.82. Ignore friction between the masses and the surface of the bowl. If the masses stick together when they collide, how high above the bottom of the bowl will they go after colliding?

Short Answer

Expert verified

The raised height for stuck blocks is R4.

Step by step solution

01

Determination of magnitude of the velocity of mass before the collisionGiven Data:

The height of the top mass from the bottom is h = R

The mass of each block is: m

02

Concept

The velocity of the top block is calculated first, then find the combined velocity of stacked mass and use energy conservation to height raised by both blocks.

The speed of the top is given as:

u=2gh

Here, g is the gravitational acceleration.

Substitute all the values in the above equation.

u=2gRu=2gR

Apply the momentum conservation to find the speed of stuck blocks.

mu=m+mvv=u2v=2gR2V=gR2

03

Determination of height raised by combined mass

Apply the energy conservation to find raised height for sticked blocks.

12m+mv2=m+mgHH=v22g

Substitute all the values in the above equation.

H=gR222gH=R4

Therefore, the raised height for sticked blocks is R4.

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