/*! 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 16 A 13-g goldfinch has a speed of ... [FREE SOLUTION] | 91Ó°ÊÓ

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A 13-g goldfinch has a speed of \(8.5 \mathrm{~m} / \mathrm{s}\). What is its kinetic energy?

Short Answer

Expert verified
The kinetic energy is approximately 0.47 Joules.

Step by step solution

01

Understanding the Formula

The kinetic energy (KE) of an object can be calculated using the formula: \[ KE = \frac{1}{2} mv^2 \] where \( m \) is the mass of the object in kilograms and \( v \) is the velocity of the object in meters per second.
02

Convert Mass to Kilograms

First, we need to convert the mass of the goldfinch from grams to kilograms since the formula uses kilograms. There are 1000 grams in a kilogram, so: \[ 13 ext{ grams} = 0.013 ext{ kilograms} \]
03

Calculate the Kinetic Energy

Now we can substitute the values into the kinetic energy formula:- \( m = 0.013 \text{ kg} \)- \( v = 8.5 \text{ m/s} \)\[ KE = \frac{1}{2} \times 0.013 \times (8.5)^2 \]\[ KE = \frac{1}{2} \times 0.013 \times 72.25 \]\[ KE = 0.0065 \times 72.25 \]\[ KE \approx 0.47 \text{ Joules} \]
04

Final Result

The kinetic energy of the goldfinch is approximately \(0.47 \text{ Joules}\).

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Key Concepts

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

Mass Conversion
When solving physics problems like calculating the kinetic energy, one often needs to deal with units. The formula for kinetic energy requires the mass of an object to be in kilograms. If you have mass in grams, like in the case of the goldfinch exercise, you'll need to convert it to kilograms. This is done because the standard unit system for physics calculations is the International System of Units (SI), where mass is measured in kilograms.

To convert grams to kilograms, use the conversion factor that there are 1000 grams in a kilogram. So for instance, if the mass of the bird is 13 grams, the conversion would be:
  • Divide 13 by 1000.
  • This results in 0.013 kilograms.
Converting units consistently helps avoid errors and ensures all parts of the formula are compatible.
Velocity
Another important component of kinetic energy calculation is velocity. Velocity refers to the speed of an object in a specified direction, measured in meters per second (m/s). It's a vector quantity, meaning it has both magnitude and direction.

In kinetic energy calculations, velocity plays a crucial role because it is squared in the formula:\[ KE = \frac{1}{2} mv^2 \]This means that even small changes in velocity result in bigger changes in kinetic energy, since the effect of velocity is "squared." When working on problems, always ensure the velocity is in meters per second, as the standard unit in SI. For example, in the goldfinch exercise, the bird's speed is given as 8.5 m/s, which can be directly used in the formula, simplifying the calculation process.
Physics Problems
Physics problems often involve applying well-defined formulas to specific scenarios, as seen with the kinetic energy problem involving a goldfinch. Solving problems like these helps to solidify understanding of physical concepts and the mathematical relationships between them.

When tackling physics problems, it's crucial to:
  • Identify what you are asked to find and the relevant formula to use. Here, it is kinetic energy and the formula for it.
  • Ensure all units are consistent with SI units, using conversion when necessary.
  • Plug the known values into the formula carefully and solve step by step to avoid mistakes.
  • Review your final answer to see if it makes sense logically.
Physics problems with step-by-step approaches can improve problem-solving skills and make concepts like kinetic energy clearer and easier to grasp.

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Most popular questions from this chapter

Calculate A kayaker paddles with a power output of \(50.0 \mathrm{~W}\) to maintain a steady speed of \(1.50 \mathrm{~m} / \mathrm{s}\). Find the force exerted by the kayaker.

A person places a cup of coffee on the roof of her car while she dashes back into the house for a forgotten item. When she returns to the car, she hops in and takes off with the coffee cup still on the roof. (a) If the coefficient of static friction between the coffee cup and the roof of the car is \(0.24\), what is the maximum acceleration the car can have without causing the cup to slide? Ignore the effects of air resistance. (b) What is the smallest amount of time in which the person can accelerate the car from rest to \(15 \mathrm{~m} / \mathrm{s}\) and still keep the coffee cup on the roof?

\(\rightarrow\) Apply The potential energy of an object decreases by \(10 \mathrm{~J}\). What is the change in the object's kinetic energy, assuming there is no friction in the system?

You jump out of an airplane and open your parachute after an extended period of free fall. (a) To decelerate your fall, must the force exerted on you by the parachute be greater than, less than, or equal to your weight? (b) Choose the best explanation from among the following: A. A parachute can only exert a force that is less than the weight of the skydiver. B. The parachute exerts a force exactly equal to the skydiver's weight. C. To decelerate a skydiver in free fall, the net force acting on the skydiver must be upward.

(a) If the force acting on an object doubles, what happens to the object's acceleration? (b) If the mass of an object doubles, what happens to the object's acceleration?

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