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Chapter 9: Problem 21

In Problem 27 of Chapter 7 you found the recoil speed of Bob as he throws a rock while standing on frictionless ice. Bob has a mass of \(75 \mathrm{kg}\) and can throw a \(500 \mathrm{g}\) rock with a speed of \(30 \mathrm{m} / \mathrm{s}\) Find Bob's recoil speed again, this time using momentum.

Short Answer

Expert verified
The recoil speed of Bob is \(0.2 \mathrm{m/s}\) in the direction opposite to the throw.

Step by step solution

01

Convert mass of rock from gram to kilogram

As the SI unit of mass is kilogram, convert the mass of the rock from gram to kilogram. So, \(0.5 \mathrm{kg}\) is the mass of the rock.
02

Compute the momentum of the system before throwing

Before throwing, the total momentum of the system (Bob and the rock) was zero because neither Bob nor the rock was in motion.
03

Compute the momentum of the rock

As per the momentum formula (momentum = mass 脳 velocity), the momentum of the thrown rock = \(0.5 \mathrm{kg} \times 30 \mathrm{m/s} = 15 \mathrm{kg路m/s}\).
04

Calculate Bob's recoil speed

By conservation of momentum principle, the momentum of Bob should be equal to the momentum of the rock but in the opposite direction. The recoil speed of Bob = \( \frac{-15 \mathrm{kg路m/s}}{75 \mathrm{kg}} = -0.2 \mathrm{m/s}\). The negative sign indicates the direction of Bob's movement, opposite to the rock's direction.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Recoil Speed
In physics, when an object hurls another object away, like Bob throwing a rock on frictionless ice, the thrower moves in the opposite direction. This movement in the opposite direction is known as recoil speed. Bob experiences recoil speed when he throws the rock. Recoil is fascinating as it demonstrates the relationship between applied force and motion.
Bob, standing still initially, feels the rate of change in motion once the rock is projected forward. His backward motion symbolizes the essence of Newton's third law: for every action, there is an equal and opposite reaction. Understanding recoil provides insights into how forces work in tandem with each other, even in our daily life like walking or swimming.
Momentum Calculation
Momentum is a fundamental concept in physics, which describes the quantity of motion an object has. Calculating momentum involves a straightforward multiplication of mass and velocity. For example, when Bob throws the rock, the momentum calculation for the rock is done using its mass and speed.
To calculate, simply multiply the mass of the rock (converted from 500 grams to 0.5 kg) by its velocity (30 m/s), giving us a rock momentum of 15 kg路m/s. This value explains how much motion the rock carries with it as it flies away. The magnitude of this momentum helps to describe how both Bob and the rock interact after the throw.
Conservation of Momentum Principle
The conservation of momentum principle states that in a closed system, the total momentum before and after an event must remain constant. So, when Bob throws the rock, both he and the rock together make up a closed system on the ice.
Initially, the total momentum is zero since neither Bob nor the rock are moving. As the rock is thrown, it gains momentum. By the principle of conservation of momentum, Bob must acquire momentum equal in magnitude but opposite in direction to the rock.
This means Bob's momentum calculates to -15 kg路m/s, effectively balancing the system. Dividing this momentum by Bob's mass (75 kg), his recoil speed becomes -0.2 m/s. The conservation of momentum ensures that the system remains balanced, highlighting how physical laws govern motion across different environments.

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