Ch 08: Momentum, Impulse, and Collisions

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook

Young & Freedman Calc 15th Edition

Ch 08: Momentum, Impulse, and Collisions

Problem 21a

Chapter 8, Problem 21a

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. What was the speed of puck A before the collision?

Verified step by step guidance

Step 1: Identify the principle of conservation of momentum. Since the collision occurs on a frictionless surface, the total momentum of the system before and after the collision is conserved. The equation for momentum conservation is:

m

₁v_1i + m₂v_2i = m₁v_1f + m₂v_2f, where

m

₁ and

m

₂ are the masses of pucks A and B, and

v

_1i,

v

_2i,

v

_1f, and

v

_2f are the initial and final velocities of pucks A and B, respectively.

Step 2: Substitute the known values into the momentum conservation equation. Given

m

₁ = 0.250 kg,

m

₂ = 0.350 kg,

v

_2i = 0 m/s (puck B is initially at rest),

v

_1f = -0.120 m/s (to the left is negative), and

v

_2f = 0.650 m/s, the equation becomes:

0.250 v

_1i + 0.350(0) = 0.250(-0.120) + 0.350(0.650).

Step 3: Solve for the initial velocity of puck A,

v

_1i. Rearrange the equation to isolate

v

_1i and calculate its value. This will give you the speed of puck A before the collision.

Step 4: To calculate the change in total kinetic energy, use the formula for kinetic energy:

K = \frac{1}{2} m v

². Compute the total kinetic energy before the collision:

K

_initial = 12m₁v_1i² + 12m₂v_2i². Then compute the total kinetic energy after the collision:

K

_final = 12m₁v_1f² + 12m₂v_2f².

Step 5: Find the change in kinetic energy by subtracting the initial kinetic energy from the final kinetic energy:

K = K

_final - K_initial. This will give you the change in the total kinetic energy of the system during the collision.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Conservation of Momentum

The principle of conservation of momentum states that in a closed system, the total momentum before an event (like a collision) is equal to the total momentum after the event. This is crucial for solving problems involving collisions, as it allows us to relate the velocities and masses of the objects involved. In this scenario, we can use the masses of the pucks and their velocities before and after the collision to find the initial speed of puck A.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, calculated using the formula KE = 0.5 * m * v^2, where m is mass and v is velocity. Understanding kinetic energy is essential for analyzing the energy changes that occur during collisions. In this problem, we need to calculate the total kinetic energy before and after the collision to determine the change in energy, which can indicate whether the collision was elastic or inelastic.

Elastic vs. Inelastic Collisions

Collisions can be classified as elastic or inelastic based on whether kinetic energy is conserved. In elastic collisions, both momentum and kinetic energy are conserved, while in inelastic collisions, momentum is conserved but kinetic energy is not. This distinction is important for analyzing the results of the collision between the pucks, as it will affect the calculations of kinetic energy change and the interpretation of the collision's nature.

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Related Practice

Textbook Question

When cars are equipped with flexible bumpers, they will bounce off each other during low-speed collisions, thus causing less damage. In one such accident, a 1750-kg car traveling to the right at 1.50 m/s collides with a 1450-kg car going to the left at 1.10 m/s. Measurements show that the heavier car's speed just after the collision was 0.250 m/s in its original direction. Ignore any road friction during the collision. Calculate the change in the combined kinetic energy of the two-car system during this collision.

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Textbook Question

Two vehicles are approaching an intersection. One is a 2500-kg pickup traveling at 14.0 m/s from east to west (the -x-direction), and the other is a 1500-kg sedan going from south to north (the +y-direction) at 23.0 m/s. What are the magnitude and direction of the net momentum?

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Textbook Question

You are standing on a sheet of ice that covers the football stadium parking lot in Buffalo; there is negligible friction between your feet and the ice. A friend throws you a 0.600-kg ball that is traveling horizontally at 10.0 m/s. Your mass is 70.0 kg. If the ball hits you and bounces off your chest, so afterward it is moving horizontally at 8.0 m/s in the opposite direction, what is your speed after the collision?

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Textbook Question

When cars are equipped with flexible bumpers, they will bounce off each other during low-speed collisions, thus causing less damage. In one such accident, a 1750-kg car traveling to the right at 1.50 m/s collides with a 1450-kg car going to the left at 1.10 m/s. Measurements show that the heavier car's speed just after the collision was 0.250 m/s in its original direction. Ignore any road friction during the collision. What was the speed of the lighter car just after the collision?

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Textbook Question

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. Calculate the change in the total kinetic energy of the system that occurs during the collision.

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Textbook Question

You are standing on a sheet of ice that covers the football stadium parking lot in Buffalo; there is negligible friction between your feet and the ice. A friend throws you a 0.600-kg ball that is traveling horizontally at 10.0 m/s. Your mass is 70.0 kg. If you catch the ball, with what speed do you and the ball move afterward?

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