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Chapter 5: Problem 19

A \(200 .-\mathrm{kg}\) moving tiger has a kinetic energy of \(14,400 \mathrm{~J}\) What is the speed of the tiger?

Short Answer

Expert verified
Answer: The speed of the 200 kg tiger with a kinetic energy of 14,400 J is 12 m/s.

Step by step solution

01

Write down the given values and formula

We are given: - Mass of the tiger (m) = 200 kg - Kinetic energy (KE) = 14,400 J We will use the kinetic energy formula: \(KE = \frac{1}{2}mv^2\)
02

Isolate the speed variable (v) in the equation

We need to find the value of 'v'. So we need to isolate 'v' in the kinetic energy formula. To do this, follow these steps: 1. Multiply both sides of the equation by 2: \(2 \times KE = 2 \times \frac{1}{2}mv^2\) 2. Simplify the equation: \(2 \times KE = mv^2\) 3. Divide both sides of the equation by m: \(\frac{2 \times KE}{m} = v^2\) Now, we have isolated the variable 'v' in the equation: \(v^2 = \frac{2 \times KE}{m}\)
03

Plug in the values and calculate the square of the speed

We will now plug in the given values of m (200 kg) and KE (14,400 J) into the equation we've just derived in step 2: \(v^2 = \frac{2 \times 14,400}{200}\) Now, calculate the value of \(v^2\): \(v^2 = 144\)
04

Find the speed (v) by taking the square root

We now have the value of the square of the speed, and we need to find the speed by taking the square root: \(v = \sqrt{144}\) Calculate the square root: \(v = 12 \,\text{m/s}\) Therefore, the speed of the tiger is 12 m/s.

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Key Concepts

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

Kinetic Energy Formula
Understanding the kinetic energy formula is essential in physics to relate the motion of objects to their energy. Kinetic energy (\textbf{KE}) is the energy possessed by an object due to its motion. The formula to calculate kinetic energy is simple yet pivotal:
. The formula is expressed as (\textbf{KE = \(\frac{1}{2}mv^2\)}), where \(m\) represents the mass of the object and \(v\) is its velocity. In practical scenarios like the moving tiger problem, this formula helps translate the given energy value into the velocity of the animal. In understanding this concept, learners can then apply the formula in various situations to find either the kinetic energy, mass, or velocity of objects in motion
.
Isolating Variables in Physics Equations
In physics, solving problems often involves equations with multiple variables. Isolating a variable means rearranging the equation such that the variable you need to find is on one side of the equation by itself. Here's a generic guide to isolate a variable:
  • Identify the variable that needs to be isolated.
  • Perform algebraic operations that 'undo' other terms from around the variable.
  • Keep the equation balanced by performing each operation on both sides.
  • Continue until the variable is isolated.
In the context of the motion of the moving tiger, we have used this process to isolate velocity (\(v\)) from the kinetic energy formula. This process included multiplying both sides by 2, then dividing by the mass, to effectively isolate \(v^2\). This step is crucial to bridge the gap from knowing the total energy to actually determining the tiger's speed, which is more tangible in understanding motion.
Solving for Speed
Many tasks in physics require us to solve for speed, providing an understanding of how fast an object is moving. Once we've isolated speed in the equation, it's a matter of substituting the known values and simplifying.

Calculating the Square of the Speed

In the kinetic energy equation, we calculate the square of the speed first because the equation includes velocity squared (\(v^2\)). Plugging in the values and solving for \(v^2\) gives us a critical intermediate step: knowing the speed squared puts us on the brink of finding the actual speed.

Finding the Actual Speed

From there, we get the speed by taking the square root of \(v^2\). Our previous steps transform a value of kinetic energy into the square of speed, and ultimately, by applying the square root, we find out the animal's speed in meters per second. This allows us to appreciate the velocity quantitively, connecting a concrete number to the concept of speed.
The practical application shown in the tiger example illustrates a common methodology for solving for speed in physics problems and will likely be a skill used repeatedly throughout a student's scientific education.

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Most popular questions from this chapter

Supppose you pull a sled with a rope that makes an angle of \(30.0^{\circ}\) to the horizontal. How much work do you do if you pull with \(25.0 \mathrm{~N}\) of force and the sled moves \(25.0 \mathrm{~m} ?\)

A car, of mass \(m,\) traveling at a speed \(v_{1}\) can brake to a stop within a distance \(d\). If the car speeds up by a factor of \(2, v_{2}=2 v_{1},\) by what factor is its stopping distance increased, assuming that the braking force \(F\) is approximately independent of the car's speed?

The damage done by a projectile on impact is correlated with its kinetic energy. Calculate and compare the kinetic energies of these three projectiles: a) a \(10.0 \mathrm{~kg}\) stone at \(30.0 \mathrm{~m} / \mathrm{s}\) b) a \(100.0 \mathrm{~g}\) baseball at \(60.0 \mathrm{~m} / \mathrm{s}\) c) a \(20.0 \mathrm{~g}\) bullet at \(300 . \mathrm{m} / \mathrm{s}\)

A bullet moving at a speed of \(153 \mathrm{~m} / \mathrm{s}\) passes through a plank of wood. After passing through the plank, its speed is \(130 \mathrm{~m} / \mathrm{s}\). Another bullet, of the same mass and size but moving at \(92 \mathrm{~m} / \mathrm{s}\), passes through an identical plank. What will this second bullet's speed be after passing through the plank? Assume that the resistance offered by the plank is independent of the speed of the bullet.

A ski jumper glides down a \(30.0^{\circ}\) slope for \(80.0 \mathrm{ft}\) before taking off from a negligibly short horizontal ramp. If the jumper's takeoff speed is \(45.0 \mathrm{ft} / \mathrm{s}\), what is the coefficient of kinetic friction between skis and slope? Would the value of the coefficient of friction be different if expressed in SI units? If yes, by how much would it differ?
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