Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Problem 15

The damage done by a projectile on impact is correlated with its kinetic energy. Calculate and compare the kinetic energies of these three projectiles: a) a \(10.0 \mathrm{~kg}\) stone at \(30.0 \mathrm{~m} / \mathrm{s}\) b) a \(100.0 \mathrm{~g}\) baseball at \(60.0 \mathrm{~m} / \mathrm{s}\) c) a \(20.0 \mathrm{~g}\) bullet at \(300 . \mathrm{m} / \mathrm{s}\)

Short Answer

Expert verified
Question: Compare the kinetic energies of the three projectiles: a 10.0 kg stone at 30.0 m/s, a 100.0 g baseball at 60.0 m/s, and a 20.0 g bullet at 300.0 m/s. Answer: The stone has the highest kinetic energy (4500 J), followed by the bullet (900 J), and lastly the baseball (180 J).

Step by step solution

01

Understand the exercise and given information

We are supposed to calculate the kinetic energies of three projectiles and compare them. We have given masses and velocities for all three projectiles: a) 10.0 kg stone at 30.0 m/s b) 100.0 g baseball at 60.0 m/s c) 20.0 g bullet at 300.0 m/s
02

Convert masses to appropriate units

Since the base unit of mass in the SI system is kilograms, we should convert the grams (baseball and bullet) to kg before calculating the kinetic energy: b) 100.0 g to kg: \(\frac{100.0}{1000}=0.1\,kg\) c) 20.0 g to kg: \(\frac{20.0}{1000}=0.02\,kg\)
03

Calculate kinetic energies

Now we can calculate the kinetic energies (\(KE = \frac{1}{2}mv^2\)) for each projectile: a) Stone: \(KE_{stone} = \frac{1}{2}(10.0\,kg)(30.0\,m/s)^2 = 4500 \,J\) b) Baseball: \(KE_{baseball} = \frac{1}{2}(0.1\,kg)(60.0\,m/s)^2 = 180\,J\) c) Bullet: \(KE_{bullet} = \frac{1}{2}(0.02\,kg)(300.0\,m/s)^2 = 900\,J\)
04

Compare the kinetic energies

We have found the kinetic energies for all projectiles, now let's compare their values: - Stone: 4500 J - Baseball: 180 J - Bullet: 900 J In comparison, the stone has the highest kinetic energy, followed by the bullet, and lastly the baseball.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

How much work do movers do (horizontally) in pushing a \(150-\mathrm{kg}\) crate \(12.3 \mathrm{~m}\) across a floor at constant speed if the coefficient of friction is \(0.70 ?\) a) 1300 J c) \(1.3 \cdot 10^{4}\) ] e) 130 ] b) 1845 J d) \(1.8 \cdot 10^{4}\) ]

While a boat is being towed at a speed of \(12 \mathrm{~m} / \mathrm{s}\), the tension in the towline is \(6.0 \mathrm{kN}\). What is the power supplied to the boat through the towline?

A driver notices that her 1000 , \(\mathrm{kg}\) car slows from \(v_{0}=\) \(90.0 \mathrm{~km} / \mathrm{h}(25.0 \mathrm{~m} / \mathrm{s})\) to \(v=70.0 \mathrm{~km} / \mathrm{h}(19.4 \mathrm{~m} / \mathrm{s})\) in \(t=6.00 \mathrm{~s}\) moving on level ground in neutral gear. Calculate the power needed to keep the car moving at a constant speed, \(v_{\text {ave }}=\) \(80.0 \mathrm{~km} / \mathrm{h}(22.2 \mathrm{~m} / \mathrm{s})\)

A force has the dependence \(F_{x}(x)=-k x^{4}\) on the displacement \(x\), where the constant \(k=20.3 \mathrm{~N} / \mathrm{m}^{4}\). How much work does it take to change the displacement from \(0.73 \mathrm{~m}\) to \(1.35 \mathrm{~m} ?\)

A particle moves parallel to the \(x\) -axis. The net force on the particle increases with \(x\) according to the formula \(F_{x}\) \(=(120 \mathrm{~N} / \mathrm{m}) x,\) where the force is in newtons when \(x\) is in meters. How much work does this force do on the particle as it moves from \(x=0\) to \(x=0.50 \mathrm{~m} ?\) a) 7.5 J c) \(30 J\) e) 120 J b) 15 J d) 60
See all solutions

Recommended explanations on Physics Textbooks

Famous Physicists

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Magnetism

Read Explanation

Fields in Physics

Read Explanation

Mechanics and Materials

Read Explanation

Atoms and Radioactivity

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free