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Chapter 3: Problem 411

A cricket ball of mass \(150 \mathrm{~g}\). is moving with a velocity of $12 \mathrm{~m} / \mathrm{s}$ and is hit by a bat so that the ball is turned back with a velocity of \(20 \mathrm{~m} / \mathrm{s}\). If duration of contact between the ball and the bat is \(0.01 \mathrm{sec}\). The impulse of the force is (A) \(7.4 \mathrm{NS}\) (B) \(4.8 \mathrm{NS}\) (C) \(1.2 \mathrm{NS}\) (D) \(4.7 \mathrm{NS}\)

Short Answer

Expert verified
The impulse of the force is (B) \(4.8 \mathrm{NS}\).

Step by step solution

01

Convert mass to kg

The mass of the cricket ball is given in grams (150g). We need to convert this to kilograms (kg) to work in the SI unit system. To convert grams to kilograms, divide by 1000. \(Mass (kg) = \frac{150}{1000} = 0.15 \ kg\)
02

Calculate initial and final momentum

Now, we can calculate the initial and final momentum of the cricket ball: \(Initial \ momentum = mass \times initial \ velocity\) \(Final \ momentum = mass \times final \ velocity\) Plug in the values for mass and velocities: \(Initial \ momentum = 0.15 \ kg \times 12 \ m/s = 1.8 \ kg \cdot m/s\) \(Final \ momentum = 0.15 \ kg \times -20 \ m/s = -3 \ kg \cdot m/s\) Notice that we used a negative sign for the final velocity since the ball is turned back.
03

Calculate the impulse

Now, we can calculate the impulse using the impulse-momentum theorem: \(Impulse = Final \ momentum - Initial \ momentum\) Plug in the values for initial and final momentum: \(Impulse = -3 \ kg \cdot m/s - 1.8 \ kg \cdot m/s = -4.8 \ kg \cdot m/s\)
04

Convert impulse to Ns (Newton-seconds)

Since impulse is the product of force and time, the units of impulse are Newton-seconds (Ns). In this case, our impulse is already in Ns, since we have kg·m/s (which is equivalent to Ns). Impulse = -4.8 Ns The negative sign means that the direction of the impulse is opposite to the initial direction of the ball.
05

Choose the correct answer

The correct answer is: (B) \(4.8 \mathrm{NS}\) Note that the answer is given as a positive value, which is referring to the magnitude of the impulse.

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Most popular questions from this chapter

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