Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

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·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 Vaia!

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—positive 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

An 8.00-kg block of wood sits at the edge of a frictionless table, 2.20 m above the floor. A 0.500-kg blob of clay slides along the length of the table with a speed of 24.0 m/s, strikes the block of wood, and sticks to it. The combined object leaves the edge of the table and travels to the floor. What horizontal distance has the combined object traveled when it reaches the floor?

For the Texas Department of Public Safety, you are investigating an accident that occurred early on a foggy morning in a remote section of the Texas Panhandle. A 2012 Prius traveling due north collided in a highway intersection with a 2013 Dodge Durango that was traveling due east. After the collision, the wreckage of the two vehicles was locked together and skidded across the level ground until it struck a tree. You measure that the tree is 35 ft from the point of impact. The line from the point of impact to the tree is in a direction 39\(^\circ\) north of east. From experience, you estimate that the coefficient of kinetic friction between the ground and the wreckage is 0.45. Shortly before the collision, a highway patrolman with a radar gun measured the speed of the Prius to be 50 mph and, according to a witness, the Prius driver made no attempt to slow down. Four people with a total weight of 460 lb were in the Durango. The only person in the Prius was the 150-lb driver. The Durango with its passengers had a weight of 6500 lb, and the Prius with its driver had a weight of 3042 lb. (a) What was the Durango's speed just before the collision? (b) How fast was the wreckage traveling just before it struck the tree?

On a frictionless, horizontal air table, puck \(A\) (with mass 0.250 kg) is moving toward puck \(B\) (with mass 0.350 kg), which is initially at rest. After the collision, puck A has a velocity of 0.120 m/s to the left, and puck \(B\) has a velocity of 0.650 m/s to the right. (a) What was the speed of puck \(A\) before the collision? (b) Calculate the change in the total kinetic energy of the system that occurs during the collision.

You are standing on a large sheet of frictionless ice and holding a large rock. In order to get off the ice, you throw the rock so it has velocity 12.0 m/s relative to the earth at an angle of 35.0\(^\circ\) above the horizontal. If your mass is 70.0 kg and the rock's mass is 3.00 kg, what is your speed after you throw the rock? (See Discussion Question Q8.7.)

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?

See all solutions

Recommended explanations on Physics Textbooks

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.

Sign-up for free