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Chapter 11: Q. 22 (page 288)

A $50 g$ marble moving at $2.0 m / s$ strikes a $20 g$ marble at rest. What is the speed of each marble immediately after the collision?

Short Answer

Expert verified

Marvel of mass $50 g$ has speed $0.86 m / s$ .

Marvel of mass $20 g$ has speed $2.9 m / s .$

Step by step solution

01

Given information

We have given,

Masses of marvel = $50 g and 20 g .$

Speed of marvels = $2 m / s and 0 m / s .$

We have to find their final velocity after collision.

02

Simplify

The given Collison is a elastic collision.

In the elastic Collison the momentum and energy of the system is conserved.

Then conservation of momentum is,

$P_{i} = P_{f}$

Let us consider marvels as marvel 1 of $50 g$ and marvel 2 of $20 g .$

Then,

$P_{i} = m_{1} v_{1} + m_{2} v_{2} P_{i} = 0.05 kg 脳 2 m / s + 0 P_{i} = 0.1 kg m / s$

and

$P_{F} = m_{1} v_{1 f} + m_{2} v_{2 f} . . . . . . . . . . (1)$

Then using conservation of energy,

localid="1649676035847" $K . E_{I} = K . E . F_{F} \frac{m_{1} v_{1}^{2} + m_{2} v_{2}^{2}}{2} = \frac{m_{1} v_{1 f}^{2} + m_{2} v_{2 f}^{2}}{2} (0.05) (4) = m_{1} v_{1 f}^{2} + m_{2} v_{2 f}^{2} . . . . . . . . . . . . . . . . . . . . . . . . (2)$

Using equation (1) AND (2),

$v_{1 f} = 0.86 m / s v_{2 f} = 2.9 m / s$

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Most popular questions from this chapter

Three identical train cars, coupled together, are rolling east at speed $v_{o}$ . A fourth car traveling east at $2 v_{o}$ catches up with the three and couples to make a four-car train. A moment later, the train cars hit a fifth car that was at rest on the tracks, and it couples to make a five-car train. What is the speed of the five-car train?

A $50 kg$ archer, standing on frictionless ice, shoots a $100 g$ arrow at a speed of $100 m / s$ . What is the recoil speed of the archer?

Far in space, where gravity is negligible, a $425 k g$ rocket traveling at $75 m / s$ fires its engines. FIGURE EX11.11 shows the thrust force as a function of time. The mass lost by the rocket during these $30 s$ is negligible.

a. What impulse does the engine impart to the rocket?

b. At what time does the rocket reach its maximum speed? What is the maximum speed?

What impulse does the force shown in FIGURE EX11.3 exert on a $250 g$ particle?

A $2 k g$ object is moving to the right with a speed of $1 m / s$ when it experiences an impulse of $4 N s$ . What are the object鈥檚 speed and direction after the impulse?

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