Ch 11: Impulse and Momentum

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 11: Impulse and Momentum

Problem 20

Chapter 11, Problem 20

A 30 g dart traveling horizontally hits and sticks in the back of a 500 g toy car, causing the car to roll forward at 1.4 m/s. What was the speed of the dart?

Verified step by step guidance

Identify the principle to use: This is a conservation of momentum problem. The total momentum before the collision equals the total momentum after the collision, as no external forces act on the system.

Write the equation for conservation of momentum:

m

₁v₁ + m₂v₂ = (m₁ + m₂)v_f, where

m

₁ and

v

₁ are the mass and velocity of the dart,

m

₂ and

v

₂ are the mass and velocity of the toy car before the collision, and

v

_f is the final velocity of the combined system.

Substitute the known values into the equation: The mass of the dart is

0.03

kg, the mass of the toy car is

0.5

kg, the initial velocity of the toy car is

0

m/s (since it is stationary), and the final velocity of the combined system is

1.4

m/s. The equation becomes:

0.03 v

₁ + 0.5(0) = (0.03 + 0.5)(1.4).

Simplify the equation: The term

0.5(0)

becomes

0

, so the equation reduces to

0.03 v

₁ = (0.53)(1.4). Solve for

v

₁ by dividing both sides by

0.03

Perform the final calculation: After isolating

v

₁, compute the value of

(0.53)(1.4)/0.03

to find the initial speed of the dart.

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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 must equal the total momentum after the event. In this scenario, the dart and the toy car form a closed system where the dart collides with the car. The momentum of the dart before the collision must equal the combined momentum of the dart and car after they stick together.

Momentum Calculation

Momentum is calculated as the product of an object's mass and its velocity (p = mv). For the dart and the toy car, we need to calculate their individual momenta before and after the collision. The dart's momentum before the collision can be expressed as the product of its mass and its unknown velocity, while the car's momentum after the collision is the product of its combined mass and the final velocity.

Inelastic Collision

An inelastic collision is a type of collision where the colliding objects stick together after the impact, resulting in a loss of kinetic energy. In this case, the dart embeds itself in the toy car, making it an inelastic collision. While momentum is conserved, kinetic energy is not, which is important to consider when analyzing the system's behavior post-collision.

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Completely Inelastic Collisions

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