/*! 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 47 A bumblebee has a mass of about ... [FREE SOLUTION] | 91Ó°ÊÓ

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A bumblebee has a mass of about \(0.25 \mathrm{~g}\). If its speed is \(10 \mathrm{~m} / \mathrm{s}\), calculate its kinetic energy. \(55 \mathrm{M}\)

Short Answer

Expert verified
The kinetic energy of the bumblebee is 0.0125 Joules.

Step by step solution

01

Convert mass to SI units

The mass given is in grams. But the SI unit for mass is the kilogram. So, we convert the mass from grams to kilograms. 1 gram is equal to 0.001 kilograms. So, the mass of the bumblebee in kg is \(0.25 * 0.001 = 0.00025 kg \)
02

Insert values into the kinetic energy formula.

The formula for kinetic energy is \(KE = \frac{1}{2}m*v^2\). Substitute the given speed of 10 m/s and the calculated mass into the kinetic energy formula. This gives \(KE = \frac{1}{2} * 0.00025 kg * (10 m/s)^2\)
03

Calculate the kinetic energy

Calculate the kinetic energy by performing the operations in the formula. You get \(KE = 0.5 * 0.00025 kg * 100 m^2/s^2 = 0.5 * 0.025 = 0.0125 Joules \) .

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Key Concepts

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

SI Units Conversion
Before diving into calculating the kinetic energy of any object, it's crucial to ensure all measurements are in the correct units. In scientific calculations, SI units, or International System of Units, are standard. For example, in this exercise, the mass of the bumblebee is given in grams. However, the SI unit for mass is the kilogram. Thus, conversion is necessary.To convert grams to kilograms, remember that:
  • 1 gram = 0.001 kilograms
So, converting the bumblebee's mass:
  • \[0.25 ext{ g} imes 0.001 = 0.00025 ext{ kg}\]
This conversion allows for consistency in calculations and prevents errors. Use this step whenever mass in grams is encountered.
Kinetic Energy Formula
Kinetic energy is the energy an object possesses due to its motion. The formula to compute kinetic energy (KE) is straightforward but powerful:\[KE = \frac{1}{2} m v^2\]Where:
  • \(m\) is the mass in kilograms.
  • \(v\) is the velocity in meters per second (m/s).
Replacing known values for the bumblebee, that is a mass of 0.00025 kg and a speed of 10 m/s, results in:
  • \[KE = \frac{1}{2} \times 0.00025 \times (10)^2\]
This step showcases how kinetic energy depends on both mass and the square of velocity. Always square the speed before continuing with the calculation.
Physics Problem Solving Step-by-Step
Solving physics problems effectively requires a systematic approach. 1. **Understand the Problem**: Read the problem carefully. Highlight what you need to find, like kinetic energy, and the information provided, such as mass and velocity. 2. **Convert Units**: Ensure all measurements are in SI units to maintain consistency. For example, convert mass from grams to kilograms. 3. **Use the Right Formula**: Identify the correct formula. Here, it's the kinetic energy formula. 4. **Substitute Values**: Insert the converted and given values into the formula. For kinetic energy, plug in mass and velocity. 5. **Calculate**: Perform the arithmetic operations. First, square the velocity, then multiply by the mass, and finally multiply by 0.5. 6. **Review**: Double-check your calculations for accuracy. Ensure your result has the correct unit, Joules for energy. By following these steps, you can neatly solve most physics problems, ensuring clarity and precision. This approach helps break down complex problems into manageable parts.

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Most popular questions from this chapter

Three clowns are trying to move a \(300-\mathrm{kg}\) crate \(12 \mathrm{~m}\) across a smooth (frictionless) floor. Moe pushes to the right with a force of \(500 \mathrm{~N}\), Larry pushes to the left with \(300 \mathrm{~N}\), and Curly pushes straight down at \(600 \mathrm{~N}\). Calculate the work done by each of the clowns.

Calc The force that acts on an object is given by \(\vec{F}=3 x \hat{i}+4 y \hat{j}\). (The multiplicative constants carry SI units.) Calculate the work done on the object by the force when the object moves from the origin \((0,0)\) to the point \((3,4)\). SSM

How much additional potential energy is stored in a spring that has a spring constant of \(15.5 \mathrm{~N} / \mathrm{m}\) if the spring starts \(10 \mathrm{~cm}\) from the equilibrium position and ends up \(15 \mathrm{~cm}\) from the equilibrium position?

A spring that has a spring constant \(k\) is cut in half. What is the spring constant for each of the two resulting springs? A. \(0.5 k\) B. \(k\) C. \(1.5 k\) D. \(2 k\) E. \(2.5 k\)

A \(20-\mathrm{g}\) object is placed against the free end of a spring (k equal to \(25 \mathrm{~N} / \mathrm{m}\) ) that is compressed \(10 \mathrm{~cm}\) (Figure 6-42). Once released, the object slides \(1.25 \mathrm{~m}\) across the tabletop and eventually lands \(1.60 \mathrm{~m}\) from the edge of the table on the floor, as shown. Is there friction between the object and the tabletop? If there is, what is the coefficient of kinetic friction? The sliding distance on the tabletop includes the 10-cm compression of the spring and the tabletop is \(1.00 \mathrm{~m}\) above the floor level.

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