/*! 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 5 One 110-kg football lineman is r... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 5

One 110-kg football lineman is running to the right at 2.75 m/s while another 125-kg lineman is running directly toward him at 2.60 m/s. What are (a) the magnitude and direction of the net momentum of these two athletes, and (b) their total kinetic energy?

Short Answer

Expert verified
(a) 22.5 kg路m/s to the left, (b) 839.38 J.

Step by step solution

01

Calculate the Momentum of Each Lineman

Momentum is calculated using the formula \( p = mv \), where \( m \) is the mass, and \( v \) is the velocity.- For the first lineman: \( p_1 = 110 \times 2.75 = 302.5 \, \text{kg}\cdot\text{m/s} \).- For the second lineman: \( p_2 = 125 \times (-2.60) = -325 \, \text{kg}\cdot\text{m/s} \) (the negative sign indicates opposite direction).
02

Determine the Net Momentum

To find the net momentum, sum the momentum of the two linemen:\[ p_{net} = p_1 + p_2 = 302.5 - 325 = -22.5 \, \text{kg}\cdot\text{m/s} \]The magnitude of the net momentum is \(|-22.5| = 22.5 \, \text{kg}\cdot\text{m/s}\) and since it is negative, its direction is the same as the second lineman (to the left).
03

Calculate the Kinetic Energy of Each Lineman

Kinetic energy is calculated using the formula \( KE = \frac{1}{2}mv^2 \).- For the first lineman: \( KE_1 = \frac{1}{2} \times 110 \times (2.75)^2 = 416.875 \, \text{J} \).- For the second lineman: \( KE_2 = \frac{1}{2} \times 125 \times (2.60)^2 = 422.5 \, \text{J} \).
04

Determine the Total Kinetic Energy

Sum the kinetic energy of both linemen:\[ KE_{total} = KE_1 + KE_2 = 416.875 + 422.5 = 839.375 \, \text{J} \]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Momentum
Momentum is a key concept in physics that describes the quantity of motion an object possesses. It is given by the product of an object's mass and its velocity: \( p = mv \). This makes momentum a vector quantity, meaning it has both magnitude and direction. When calculating momentum, you must consider the direction of movement鈥攑ositive for one direction and negative for the opposite. In the case of the two linemen coliding, each has their own momentum based on their mass and speed. With the first lineman moving to the right and the second moving to the left, their momenta will have opposite signs. Being able to compute momentum accurately helps predict how these forces interact during collisions.
Kinetic Energy
Kinetic Energy is the energy an object has due to its motion. It's calculated using the formula \( KE = \frac{1}{2}mv^2 \), where \( m \) is the mass, and \( v \) is the velocity of the object.Understanding kinetic energy is important because it quantifies the amount of work an object can do due to its motion. In the example of the two linemen, each has energy based on their speed and mass. The faster and heavier a person (or object) is, the more kinetic energy they possess. Summing up their kinetic energies gives the total energy available just before they collide.
Conservation of Momentum
The principle of conservation of momentum states that in a closed system, with no external forces, the total momentum before and after an event remains constant. This is crucial in collision physics, where understanding momentum helps determine the results of collisions. In the scenario of the colliding linemen, despite their individual momentum values being different, their combined momentum can help predict the outcome post-collision. Even though they are moving towards each other, their net momentum indicates the direction the result of the collision will lead.
Collision Physics
Collision physics examines how objects interact when they crash into each other. Two key factors govern these interactions:
  • Momentum: Dictates the direction and magnitude of the resulting motion.
  • Kinetic Energy: Determines the potential damage or energy transfer during the impact.
In perfectly elastic collisions, both momentum and kinetic energy are conserved. But real-world collisions often involve energy transformations, meaning kinetic energy is not fully conserved due to factors like friction or deformation. Understanding these interactions helps in analyzing how the two linemen, with given masses and velocities, interact during their eventual meeting.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Just before it is struck by a racket, a tennis ball weighing 0.560 N has a velocity of \((20.0 m/s)\hat{\imath} - (4.0 m/s)\hat{\jmath}\). During the 3.00 ms that the racket and ball are in contact, the net force on the ball is constant and equal to \(-(380 N)\hat{\imath} + (110 N)\hat{\jmath}\). What are the \(x\)- and \(y\)-components (a) of the impulse of the net force applied to the ball; (b) of the final velocity of the ball?

You are at the controls of a particle accelerator, sending a beam of 1.50 \(\times\) 10\(^7\) m/s protons (mass \(m\)) at a gas target of an unknown element. Your detector tells you that some protons bounce straight back after a collision with one of the nuclei of the unknown element. All such protons rebound with a speed of 1.20 \(\times\) 10\(^7\) m/s. Assume that the initial speed of the target nucleus is negligible and the collision is elastic. (a) Find the mass of one nucleus of the unknown element. Express your answer in terms of the proton mass m. (b) What is the speed of the unknown nucleus immediately after such a collision?

A 15.0-kg fish swimming at 1.10 m/s suddenly gobbles up a 4.50-kg fish that is initially stationary. Ignore any drag effects of the water. (a) Find the speed of the large fish just after it eats the small one. (b) How much mechanical energy was dissipated during this meal?

A 15.0-kg block is attached to a very light horizontal spring of force constant 500.0 N>m and is resting on a frictionless horizontal table (\(\textbf{Fig. E8.44}\)). Suddenly it is struck by a 3.00-kg stone traveling horizontally at 8.00 m/s to the right, whereupon the stone rebounds at 2.00 m/s horizontally to the left. Find the maximum distance that the block will compress the spring after the collision.

A 0.150-kg glider is moving to the right with a speed of 0.80 m/s on a frictionless, horizontal air track. The glider has a head-on collision with a 0.300-kg glider that is moving to the left with a speed of 2.20 m/s. Find the final velocity (magnitude and direction) of each glider if the collision is elastic.
See all solutions

Recommended explanations on Physics Textbooks

Rotational Dynamics

Read Explanation

Turning Points in Physics

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Electricity

Read Explanation

Atoms and Radioactivity

Read Explanation

Torque and Rotational Motion

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.