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Calculate A \(0.27-\mathrm{kg}\) volleyball has a kinetic energy of \(7.8 \mathrm{~J}\). What is the speed of the volleyball?

Short Answer

Expert verified
The speed of the volleyball is approximately 7.6 m/s.

Step by step solution

01

Understanding Kinetic Energy Formula

The kinetic energy (KE) of an object is given by the formula \( KE = \frac{1}{2} m v^2 \), where \( m \) is the mass of the object and \( v \) is its velocity or speed. We need to solve this formula for \( v \).
02

Rearrange the Formula to Solve for Velocity

Starting with the kinetic energy formula \( KE = \frac{1}{2} m v^2 \), we solve for speed \( v \). Rearranging gives \( v^2 = \frac{2 \times KE}{m} \).
03

Substitute Known Values

Substitute the given values into the rearranged formula. Here \( KE = 7.8 \text{ J} \) and \( m = 0.27 \text{ kg} \). Thus, \( v^2 = \frac{2 \times 7.8}{0.27} \).
04

Calculate the Square of the Velocity

Calculate \( v^2 = \frac{15.6}{0.27} = 57.78 \).
05

Calculate the Velocity

Find the velocity by taking the square root of \( 57.78 \). Hence, \( v = \sqrt{57.78} \approx 7.6 \text{ m/s} \).

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Key Concepts

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

Speed Calculation
When we talk about speed calculation in physics problems, it often involves determining how quickly an object moves from one point to another. Speed is a scalar quantity, meaning it does not have a direction—it simply measures how fast something is moving. To calculate speed, you generally use the formula:
  • The basic formula for speed is:\[\text{Speed} = \frac{\text{Distance}}{\text{Time}}\]
However, in scenarios involving kinetic energy, such as in our volleyball example, we need to use a different approach.Here, the speed is derived from kinetic energy, where the formula:\[v^2 = \frac{2 \, KE}{m}\]allows us to calculate the square of the speed. To find speed \( v \), take the square root of both sides of this equation.
Physics Problems
Physics problems often involve applying key concepts of energy, force, and motion to find unknown quantities. In the exercise about the volleyball, we are exploring the concept of kinetic energy, which is the energy an object holds due to its motion. When approaching physics problems, follow these tips for better understanding:
  • Carefully read the problem to understand what is given and what needs to be found. Identify known values and the quantities to solve.
  • Apply relevant physics formulas that connect the given values with the unknowns.
  • Check units of measurement to ensure your calculations use consistent units throughout.
Such systematic approaches help break down complex problems into manageable steps, as seen in our volleyball speed calculation.
Energy Formulas
Energy formulas are key tools in physics that allow scientists and students alike to quantify how energy moves and changes form. In kinetic energy problems, we use specific formulas to express how mass and speed relate to the energy of motion.Kinetic energy, represented as:\[KE = \frac{1}{2} m v^2\]where \( KE \) is kinetic energy, \( m \) is mass, and \( v \) is velocity. This formula shows that kinetic energy increases with both mass and speed. High speed and large mass lead to higher kinetic energy.In our example, rearranging the formula helped us find the speed of the volleyball when its kinetic energy and mass are known. Such rearrangements highlight the versatile nature of physics formulas in solving diverse problems.

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Most popular questions from this chapter

Think \& Calculate A pitcher accelerates a 0.14-kg hardball from rest to \(25.5 \mathrm{~m} / \mathrm{s}\) in \(0.075 \mathrm{~s}\). (a) How much work does the pitcher do on the ball? (b) What is the pitcher's power output during the pitch? (c) Suppose the ball reaches \(25.5 \mathrm{~m} / \mathrm{s}\) in less than \(0.075 \mathrm{~s}\). Is the power produced by the pitcher in this case more than, less than, or the same as the power found in part (b)? Explain.

A child pulls a friend in a little red wagon. If the child pulls with a force of \(16 \mathrm{~N}\) for \(12 \mathrm{~m}\) and the handle of the wagon is inclined at an angle of \(25^{\circ}\) above the horizontal, how much work does the child do on the wagon?

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.

How far must a spring with a spring constant of 85 N>m be stretched to store 0.22 J of potential energy?

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?

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