/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 28 A steel ball of volume \(0.02 \m... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 28

A steel ball of volume \(0.02 \mathrm{~m}^{3}\) is sinking at a speed of \(10 \mathrm{~m} / \mathrm{s}\) in a closed jar filled with a liquid of density \(2000 \mathrm{~kg} / \mathrm{m}^{3}\). The momentum of the liquid is (A) \(400 \mathrm{~N} / \mathrm{s}\) (B) \(200 \mathrm{~N} / \mathrm{s}\) (C) \(100 \mathrm{~N} / \mathrm{s}\) (D) \(300 \mathrm{~N} / \mathrm{s}\)

Short Answer

Expert verified
The short answer for this problem is: Calculate the mass of the liquid displaced (40 kg) and then multiply it by the velocity of the liquid (-10 m/s). The momentum of the liquid is \(400 \mathrm{~N\cdot s}\) in magnitude. The correct answer is (A) \(400 \mathrm{~N/s}\).

Step by step solution

01

Calculate the mass of the steel ball

The density of steel can be taken as roughly \(7850 \mathrm{~kg/m^3}\). Therefore, the mass of the steel ball can be calculated as: mass = density 脳 volume \(m_{ball} = \rho_{steel} \times V_{ball}\) \(m_{ball} = 7850 \mathrm{~kg/m^3} \times 0.02 \mathrm{~m^3}\) \(m_{ball} = 157 \mathrm{~kg}\)
02

Calculate the volume of liquid displaced

The volume of liquid displaced is equal to the volume of the steel ball. \(V_{liquid\_displaced} = V_{ball} = 0.02 \mathrm{~m^3}\)
03

Calculate the mass of liquid displaced

Use the density of the liquid and the volume of the liquid displaced to calculate the mass of the liquid displaced. \(m_{liquid\_displaced} = \rho_{liquid} \times V_{liquid\_displaced}\) \(m_{liquid\_displaced} = 2000 \mathrm{~kg/m^3} \times 0.02 \mathrm{~m^3}\) \(m_{liquid\_displaced} = 40 \mathrm{~kg}\)
04

Calculate the momentum of the liquid

The momentum of the liquid is equal to the mass of the displaced liquid multiplied by the velocity. Since the liquid is moving in the opposite direction of the steel ball, the velocity will be -10 m/s. momentum = mass 脳 velocity \(p_{liquid} = m_{liquid\_displaced} \times v_{liquid}\) \(p_{liquid} = 40 \mathrm{~kg} \times (-10 \mathrm{~m/s})\) \(p_{liquid} = -400 \mathrm{~N\cdot s}\) The negative sign indicates that the momentum of the liquid is in the opposite direction of the steel ball. However, we're only interested in the magnitude of the momentum, so the answer is 400 N鈰卻. The correct answer is (A) \(400 \mathrm{~N/s}\).

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Most popular questions from this chapter

A ball of mass \(m\) approaches a wall of mass \(M(\gg>m)\) with speed \(4 \mathrm{~m} / \mathrm{s}\) along the normal to the wall. The speed of wall is \(1 \mathrm{~m} / \mathrm{s}\) towards the ball. The speed of the ball after an elastic collision with the wall is (A) \(5 \mathrm{~m} / \mathrm{s}\) away from the wall. (B) \(9 \mathrm{~m} / \mathrm{s}\) away from the wall. (C) \(3 \mathrm{~m} / \mathrm{s}\) away from the wall. (D) \(6 \mathrm{~m} / \mathrm{s}\) away from the wall.

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