A railroad handcar is moving along straight, frictionless...

A railroad handcar is moving along straight, frictionless tracks with negligible air resistance. In the following cases, the car initially has a total mass (car and contents) of $200 \mathrm{~kg}$ and is traveling east with a velocity of magnitude $5.00 \mathrm{~m} / \mathrm{s}$. Find the final velocity of the car in cach casc, assuming that the handcar docs not leave the tracks. (a) A $25.0 \mathrm{~kg}$ mass is thrown sideways out of the car with a velocity of magnitude $2.00 \mathrm{~m} / \mathrm{s}$ relative to the car's initial velocity, (b) $\mathrm{A} 25.0 \mathrm{~kg}$ mass is thrown backward out of the car with a velocity of $5.00 \mathrm{~m} / \mathrm{s}$ relative to the initial motion of the car. (c) A $25.0 \mathrm{~kg}$ mass is thrown into the car with a velocity of $6.00 \mathrm{~m} / \mathrm{s}$ relative to the ground and opposite in direction to the initial velocity of the car.

Key Concepts

Vector Decomposition

Because momentum is a vector quantity, it is important to analyze its components in different directions. Decomposing the momentum into orthogonal components (such as east-west and perpendicular directions) allows for proper application of conservation laws when actions occur in different directions.

Conservation of Linear Momentum

In an isolated system with no external forces acting on it, the total linear momentum remains constant. This principle is used to determine how the velocity of the handcar changes when masses are added to or ejected from the system, ensuring that the momentum before and after an event is equal.

Relative Velocity

Relative velocity refers to the speed and direction of an object as measured from a specific moving reference frame. In scenarios where masses are thrown from the handcar, understanding their velocity relative to the car is essential for accurately applying momentum conservation.

Transcript

00:01 In this problem, we have given a railroad hand car is moving along a straight frictionless track with negligible air -distance.

00:12 And car has total mass 200 kg.

00:18 Now, we have to find the final velocity of the car in each case.

00:23 In first case, a 25 kg mass is thrown sideways out of the car with a velocity of magnitude 2 meter per second related to the car's initial velocity.

00:35 So suppose we have a car like this, it has velocity of 5 meter per second related to the ground.

00:51 So we have to find if 25 kg mass is thrown sideways out of the car.

00:58 That means here 25 kg mass is this total mass of car plus 25 kg is equal to 200.

01:09 That means mass of car is 175 kg right so when 25 kg mass is thrown sideways like this sideways with 2 meter per second relative to the car's initial velocity we have to find the velocity of car final velocity of car so initially here we will conserve the momentum in x direction only right in x direction we will conserve the momentum so initially momentum is total mass is 200 and the speed is 5 this will be equal to the mass of which is thrown is 25 kg and its speed in x direction is 5 meter per second plus 175 mass of car into v.

02:07 So from here we can find the value of v.

02:10 That means the value of cars speed after the action.

02:16 So this will be equal to 5 meter per second.

02:20 This is our answer for part a.

02:23 Now in part b it is given that suppose this is a car and 25 kg mass is thrown backward out of the curve like this with a speed of 5 meter per second relative to the initial motion of car.

02:46 So we know that initial motion is 5 meter per second.

02:50 So the velocity of this throne, the velocity of this object with respect to ground will be 5 minus 5, 0 meter per second...

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