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Chapter 7: Problem 11

A silver Camry is driving on the freeway at a constant 70 mph. Another Camry, identical but white, is on the onramp and is speeding up at a rate of 5 mph per second. Compare their kinetic energies at the instant the white Camry reaches 70 mph.

Short Answer

Expert verified
The kinetic energies of both Camrys are equal when the white Camry reaches 70 mph.

Step by step solution

01

Define Kinetic Energy

Kinetic energy (K.E.) is defined by the equation: K.E.=1/2 mv^2, where m is the mass of the object and v is its velocity.
02

Identify Known Variables

Both Camrys have the same mass (m), and we will denote this mass as m. The silver Camry's velocity (v_{silver}) is 70 mph. The white Camry, at the moment in question, has reached the same velocity (v_{white} = 70 mph).
03

Convert Speeds to Consistent Units

70 mph should be converted to the same unit system used in the kinetic energy formula. We convert 70 mph to feet per second (1 mph = 1.467 ft/s): 70 mph 脳 1.467 (ft/s per mph) 鈮� 102.69 ft/s. So, v_{silver} = v_{white} = 102.69 ft/s.
04

Calculate Kinetic Energy of the Silver Camry

Using the kinetic energy formula, substitute the values for the silver Camry: K.E._{silver} = 1/2 m (102.69)^2.
05

Calculate Kinetic Energy of the White Camry

Similarly, calculate the kinetic energy for the white Camry: K.E._{white} = 1/2 m (102.69)^2.
06

Compare the Kinetic Energies

Since both kinetic energy expressions have the same mass (m) and the same velocity (102.69 ft/s), the kinetic energies of both Camrys are identical. Thus, K.E._{white} = K.E._{silver}.

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Key Concepts

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

kinetic energy formula
Kinetic energy is a crucial concept in physics that helps us understand how the motion of an object relates to its energy. The formula for kinetic energy is given by:
\( K.E. = \frac{1}{2} mv^2 \)
where \( m \) represents the mass of the object, and \( v \) stands for its velocity. This formula tells us that kinetic energy depends on both the mass and the square of the velocity. Therefore, an increase in either the mass or velocity will lead to a rise in kinetic energy. Understanding this relationship is key to solving many physics problems, including those involving moving cars like the Camrys in our exercise.
velocity conversion
When working with physics problems, it's often necessary to convert units to ensure consistency and accuracy. In our exercise, we had to convert the velocity of the Camrys from miles per hour (mph) to feet per second (ft/s). The conversion factor for this is:
\( 1 \text{ mph} = 1.467 \text{ ft/s} \)
To convert 70 mph to ft/s, we multiply by the conversion factor:
70 mph \( \times 1.467 \text{ ft/s per mph} = 102.69 \text{ ft/s} \)
Using consistent units, like ft/s in the kinetic energy formula, ensures we can accurately compare the kinetic energies of the two Camrys.
physics problem-solving
Solving physics problems often involves a systematic approach:
1. Understand the problem and identify what is being asked.
2. Write down known values and relevant equations.
3. Convert units if necessary to ensure consistency.
4. Substitute known values into equations and solve.
In our exercise, we began by identifying the kinetic energy formula and known variables. Then, we converted velocity units to ensure consistent calculations. Finally, we substituted these values into the formula and found that both Camrys have the same kinetic energy at the given moment.
units of measurement
In physics, the choice of units is essential for accurate calculations and comparisons. We often use different units for measuring various quantities like distance, time, mass, and velocity. In our exercise:
1. Distance is measured in feet (ft).
2. Time is measured in seconds (s).
The consistent use of these units allows us to apply formulas like kinetic energy correctly. Conversion between units, such as mph to ft/s, is necessary when different units are initially provided. Understanding the importance of units helps avoid errors and ensures scientific accuracy in calculations.

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Most popular questions from this chapter

You reach out a second-story window that is 5 m above the sidewalk and throw a 0.1 -kg ball straight upward with \(6 \mathrm{J}\) of kinetic energy. a. What is the ball's gravitational potential energy when it is released? b. What is the ball's gravitational potential energy just before hitting the sidewalk? c. What is the ball's kinetic energy just before hitting the sidewalk? d. How would the answer to part (c) change if the ball had initially been thrown straight down with \(6 \mathrm{J}\) of kinetic energy?

If a \(0.5-\mathrm{kg}\) ball is dropped from a height of \(6 \mathrm{m},\) what is its kinetic energy when it hits the ground?

A physics textbook is launched up a rough incline with a kinetic energy of 200 joules. When the book comes momentarily to rest near the top of the incline, it has gained 180 joules of gravitational potential energy. How much kinetic energy will it have when it returns to the launch point?

Two cars have different masses but the same kinetic energies. If the same frictional force is used to stop each car, which car, if either, will stop in the shorter distance?

In tryouts for the national bobsled team, each competing team pushes a sled along a level, smooth surface for 5 meters. One team brings a sled that is much lighter than all the others. Assuming that each team pushes with the same net force, compare the kinetic energy of the light sled to that of the others after 5 meters. Compare the momentum of the light sled to that of the others after 5 meters. (Hint: Think about the times involved.)
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