/*! 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 17 The kinetic energy of a small bo... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 17

The kinetic energy of a small boat is 15,000 J. If the boat鈥檚 speed is 5.0 m>s, what is its mass?

Short Answer

Expert verified
The mass of the boat is 1,200 kg.

Step by step solution

01

Understand the kinetic energy formula

The formula for kinetic energy is given by \( KE = \frac{1}{2} m v^2 \), where \( KE \) is the kinetic energy, \( m \) is the mass of the object, and \( v \) is its velocity. We will use this formula to find the mass of the boat.
02

Plug in the known values

We know the kinetic energy \( KE = 15,000 \) J and the velocity \( v = 5.0 \) m/s. Substituting these into the formula, we have \( 15,000 = \frac{1}{2} m (5.0)^2 \).
03

Simplify the equation

Calculate \( v^2 = (5.0)^2 = 25 \). Therefore, the equation becomes \( 15,000 = \frac{1}{2} m \times 25 \). Simplify the right side to \( \frac{25}{2} m \).
04

Solve for mass \( m \)

Rearrange the equation to solve for \( m \): \( m = \frac{15,000}{12.5} \), which simplifies to \( m = 1,200 \).
05

Verify the calculation

Plug the calculated mass back into the kinetic energy formula to ensure that \( 15,000 = \frac{1}{2} (1,200)(5.0)^2 \) to verify correctness. The calculation holds true.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Mass Calculation
In physics, calculating mass involves using given data and known formulas. In our exercise, the kinetic energy of the boat is given as 15,000 Joules, and we need to find the boat's mass. We do this by rearranging the kinetic energy formula, which is initially expressed as:
\[ KE = \frac{1}{2} m v^2 \]
Given the speed \( v \) of the boat is 5.0 m/s, we substitute our known values into this equation and solve for \( m \), the mass. This is a common technique in physics that hinges on algebraic manipulation to isolate the variable of interest.
  • Always substitute known values accurately into the equation to maintain computational integrity.
  • Apply inverse operations to solve for the desired unknown variable.
By substituting the kinetic energy and the speed into the equation, we effectively isolate mass, giving us the calculated mass of the boat.
Physics Equations
Physics equations are fundamental for translating real-world scenarios into mathematical models. In this exercise, the kinetic energy equation serves as a bridge between the physical situation of a moving boat and its mathematical representation. The equation
\[ KE = \frac{1}{2} m v^2 \]
relates three key parameters: kinetic energy (\( KE \)), mass (\( m \)), and velocity (\( v \)). Here are some ideas to consider:
  • Kinetic Energy: The energy an object possesses due to its motion.
  • Velocity Squared: This part of the equation, \( v^2 \), emphasizes how velocity affects energy, squared terms amplify its impact.
  • Mass Relationship: The mass directly influences the kinetic energy when velocity is considered; a higher mass means more energy if velocity stays the same.
Understanding and manipulating these relationships allows us to solve problems effectively by filling in known quantities and solving for unknowns.
Problem Solving Steps
Approaching physics problems systematically is crucial for reliable results. In the kinetic energy exercise, the process is broken down into manageable steps, making it easier.
  • Identify and Write the Formula: Start with the relevant physics equation. In our case, it鈥檚 the kinetic energy formula.
  • Substitute Known Values: Place provided numbers into the formula's corresponding variables. Here, we used 15,000 J for KE and 5.0 m/s for velocity.
  • Simplify and Rearrange: Break down complex expressions (e.g., \(v^2 = 25\)) and simplify the equation to isolate the desired variable, \( m \).
  • Solve for the Unknown: Execute the rearranged formula to find your solution, ensuring all steps use correct units and arithmetic.
  • Verify Results: Substitute back to check accuracy, confirming calculations yield the original provided values.
Following these steps consistently ensures that solutions are not only correct but also documented for ease of understanding in the future.

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

In a tennis match a player wins a point by hitting the \(0.059-\mathrm{kg}\) ball sharply to the ground on the opponent's side of the net. If the ball bounces upward from the ground with a speed of \(16 \mathrm{~m} / \mathrm{s}\) and is caught by a fan in the stands when it has a speed of \(12 \mathrm{~m} / \mathrm{s}\), how high above the court is the fan? Ignore air resistance.

An 1865-kg airplane starts at rest on an airport runway at sea level. What is the change in mechanical energy of the airplane if it climbs to a cruising altitude of \(2420 \mathrm{~m}\) and maintains a constant speed of \(96.5 \mathrm{~m} / \mathrm{s}\) ?

Calculate To move a suitcase up to the check-in stand at an airport, a student pushes with a horizontal force through a distance of 0.95 m. If the work done by the student is 32 J, what is the magnitude of the force he exerts?

After hitting a long fly ball that goes over the right fielder's head and lands in the outfield, a batter decides to keep going past second base and try for third base. The \(62-\mathrm{kg}\) player begins sliding \(3.4 \mathrm{~m}\) from the base with a speed of \(4.5 \mathrm{~m} / \mathrm{s}\). (a) If the player comes to rest at third base, how much work was done on the player by friction with the ground? (b) What was the coefficient of kinetic friction between the player and the ground?

Think \& Calculate A grandfather clock is powered by the descent of a \(4.35-\mathrm{kg}\) weight. (a) If the weight descends through a distance of \(0.760 \mathrm{~m}\) in \(3.25\) days, how much power does it deliver to the clock? (b) To increase the power delivered to the clock, should the time it takes for the mass to descend be increased or decreased? Explain.
See all solutions

Recommended explanations on Physics Textbooks

Dynamics

Read Explanation

Nuclear Physics

Read Explanation

Electric Charge Field and Potential

Read Explanation

Radiation

Read Explanation

Fluids

Read Explanation

Measurements

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.