/*! 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 17 A water-skier is being pulled by... [FREE SOLUTION] | 91影视

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Chapter 6: Problem 17

A water-skier is being pulled by a tow rope attached to a boat. As the driver pushes the throttle forward, the skier accelerates. A 70.3-kg water-skier has an initial speed of 6.10 m/s. Later, the speed increases to 11.3 m/s. Determine the work done by the net external force acting on the skier.

Short Answer

Expert verified
The work done is equal to the change in kinetic energy, calculated as \( W = \Delta KE \).

Step by step solution

01

Identify the Given Values

First, let's note down the values given in the problem. The mass of the water-skier \( m = 70.3 \) kg, the initial speed \( v_i = 6.10 \) m/s, and the final speed \( v_f = 11.3 \) m/s. Our goal is to calculate the work done by the net external force.
02

Recall the Work-Energy Principle

The work-energy principle states that the work done by the net force acting on an object is equal to the change in its kinetic energy. The formula is: \( W = \Delta KE = KE_f - KE_i \), where \( KE \) is the kinetic energy.
03

Calculate Initial Kinetic Energy

The initial kinetic energy \( KE_i \) can be calculated using the formula \( KE = \frac{1}{2}mv^2 \). So, \( KE_i = \frac{1}{2}(70.3) \times (6.10)^2 \). Calculate this value.
04

Calculate Final Kinetic Energy

Similarly, calculate the final kinetic energy \( KE_f \) using the formula \( KE = \frac{1}{2}mv^2 \). Therefore, \( KE_f = \frac{1}{2}(70.3) \times (11.3)^2 \). Calculate this value as well.
05

Determine the Change in Kinetic Energy

Find the change in kinetic energy \( \Delta KE = KE_f - KE_i \). Substitute the values for \( KE_f \) and \( KE_i \) obtained from steps 3 and 4 to find \( \Delta KE \).
06

Calculate the Work Done

Since the work done \( W \) is equal to the change in kinetic energy, use \( W = \Delta KE \) to find the work done by the net external force.

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Key Concepts

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

Kinetic Energy
Kinetic energy is the energy an object possesses due to its motion. It is one of the most important concepts in physics, especially when studying the dynamics of moving objects. This energy 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 its speed in meters per second. Understanding how changes in speed affect kinetic energy is crucial. For instance, in the case of the water-skier, as his speed increases from 6.10 m/s to 11.3 m/s, his kinetic energy increases as well. The relationship between speed and kinetic energy is quadratic, meaning that even a small change in speed will result in a significant change in kinetic energy.
Net Force
Net force refers to the total force acting on an object when all individual forces are combined. It plays a pivotal role in motion and is described by Newton's second law, which states that the force exerted on an object equals the mass of the object times its acceleration \( F = ma \). In the context of our water-skier, the net force is what causes the skier to accelerate as the boat pulls him forward. The culmination of all forces, including friction and the tension in the tow rope, leads to a net force that causes the skier to move faster. Recognizing that net force is linked to changes in motion is essential for solving physics problems like these.
Change in Speed
Change in speed is a key factor when considering motion and energy. It is defined as the difference between the final speed and the initial speed of an object. In our example, the water-skier's speed changes from 6.10 m/s to 11.3 m/s. This increase in speed is directly related to the work done by the net force on the skier, resulting in a corresponding increase in kinetic energy. The change in speed can be calculated as:\[ \Delta v = v_f - v_i \] where \( v_f \) is the final speed and \( v_i \) is the initial speed. Understanding how changes in speed affect kinetic energy and motion helps in analyzing real-life scenarios and solving physics problems effectively.
Physics Problem Solving
Physics problem solving involves a step-by-step approach to find solutions to complex problems. Let's break down the process with our example of the water-skier.
  • First, identify the known values such as mass, initial speed, and final speed.
  • Recall the relevant physics principles, like the work-energy principle in this case.
  • Use formulas to calculate key quantities, such as initial and final kinetic energy.
  • Determine the change in kinetic energy to find the work done.
By analyzing each aspect methodically, physics problems become more manageable. This structured approach not only provides understanding but also helps in developing problem-solving skills applicable beyond physics.

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Most popular questions from this chapter

The hammer throw is a track-and-field event in which a 7.3-kg ball (the 鈥渉ammer鈥�), starting from rest, is whirled around in a circle several times and released. It then moves upward on the familiar curving path of projectile motion. In one throw, the hammer is given a speed of 29 m/s. For comparison, a .22 caliber bullet has a mass of 2.6 g and, starting from rest, exits the barrel of a gun at a speed of 410 m/s. Determine the work done to launch the motion of (a) the hammer and (b) the bullet.

A 67.0-kg person jumps from rest off a 3.00-m-high tower straight down into the water. Neglect air resistance. She comes to rest 1.10 m under the surface of the water. Determine the magnitude of the average force that the water exerts on the diver. This force is non conservative.

A pendulum consists of a small object hanging from the ceiling at the end of a string of negligible mass. The string has a length of 0.75 m. With the string hanging vertically, the object is given an initial velocity of 2.0 m/s parallel to the ground and swings upward on a circular arc. Eventually, the object comes to a momentary halt at a point where the string makes an angle \(\theta\) with its initial vertical orientation and then swings back downward. Find the angle \(\theta\) .

The (non conservative) force propelling a \(1.50 \times 10^{3}-kg\) car up a mountain road does \(4.70 \times 10^{6} J\) of work on the car. The car starts from rest at sea level and has a speed of 27.0 \(m /s\) sat an altitude of \(2.00 \times 10^{2} m\) above sea level. Obtain the work done on the car by the combined forces of friction and air resistance, both of which are non conservative forces.

A pitcher throws a \(0.140-kg\) baseball, and it approaches the bat at a speed of 40.0 \(m/s\) . The bat does \(W_{\mathrm{nc}}=70.0 J\) of work on the ball in hitting it. Ignoring air resistance, determine the speed of the ball after the ball leaves the bat and is 25.0 \(m\) above the point of impact.
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