Conservation of Momentum Physics Problems - Basic Introduction

Summary

This video explains the concept of conservation of momentum through three practical problems. The first involves an astronaut throwing a ball, where momentum is conserved between the astronaut and the ball, resulting in the astronaut moving in the opposite direction. The second problem discusses an object exploding into two fragments, with momentum transferred between them. The third example involves a moving railroad cart and a rock dropped into it, showing how momentum is transferred to the rock while slowing the cart down. The video highlights how momentum remains constant in isolated systems, and how mass and velocity interact in these scenarios.

Takeaways

• 😀 The law of conservation of momentum states that the total momentum before an event equals the total momentum after the event.
• 😀 When an astronaut throws a ball, the astronaut moves in the opposite direction due to the conservation of momentum.
• 😀 The momentum before the throw (when both the astronaut and ball are at rest) is zero, and after the throw, the total momentum is still zero.
• 😀 The astronaut's velocity after throwing the ball is slower than the ball's velocity because the astronaut has more mass.
• 😀 In an explosion, momentum is conserved. The momentum of the system before the explosion is zero if the object was at rest.
• 😀 The velocity of the smaller fragment in an explosion will be greater than that of the larger fragment, as momentum is transferred between them.
• 😀 When a rock is dropped into a moving railroad cart, the cart’s velocity decreases due to the rock’s momentum being added to the system.
• 😀 The total momentum of a system is conserved even when mass is added to it, such as a rock falling into a cart.
• 😀 The final velocity of the combined cart and rock is lower than the initial velocity of the cart because the total mass has increased.
• 😀 Momentum is transferred between objects when they interact, as seen when the cart slows down and the rock speeds up after the rock is dropped in.
• 😀 As mass increases while momentum is conserved, the velocity of the system decreases, which is observed in the cart-rock example.

Q & A

What is the principle of conservation of momentum?

The principle of conservation of momentum states that the total momentum of a closed system before an event (such as a collision or explosion) is equal to the total momentum of the system after the event, as long as no external forces are acting on it.

How does Newton's third law apply to the astronaut and ball problem?

Newton's third law states that for every action, there is an equal and opposite reaction. When the astronaut throws the ball, the ball exerts a force on the astronaut, causing the astronaut to move in the opposite direction. This is why the astronaut moves west while the ball moves east.

Why is the astronaut's velocity lower than the ball's velocity after throwing it?

The astronaut has a much larger mass compared to the ball, so, according to the conservation of momentum, the astronaut's velocity is lower. The ball, being lighter, moves faster because momentum is conserved but the mass difference causes a disparity in velocity.

In the exploding object example, why does the smaller fragment move faster than the larger one?

In an explosion, the total momentum of the system must remain zero (since the object was initially at rest). Since the larger fragment has more mass, it moves slower, while the smaller fragment moves faster to conserve the total momentum.

What happens when a rock is dropped into a moving railroad cart, according to the conservation of momentum?

When the rock is dropped into the moving cart, the total momentum of the system is conserved. As the rock accelerates in the x-direction (matching the cart's velocity), the cart slows down due to the transfer of momentum to the rock. The combined speed of the cart and the rock is less than the initial speed of the cart alone.

Why does the final speed of the railroad cart decrease when the rock is added?

The mass of the system increases when the rock is added, and since momentum is conserved, the combined velocity of the cart and rock must decrease. The momentum of the cart is shared between the cart and the rock, leading to a decrease in the cart's speed.

What does the negative sign in the astronaut's velocity indicate in the first example?

The negative sign in the astronaut's velocity indicates that the astronaut is moving in the opposite direction of the ball, i.e., west, as per the reaction force described by Newton's third law.

How do the mass and velocity of objects relate when momentum is conserved?

When momentum is conserved, the mass of an object and its velocity are inversely proportional. An object with more mass moves slower, while an object with less mass moves faster, assuming the total momentum of the system is conserved.

How does the momentum transfer occur between the railroad cart and the rock?

The railroad cart exerts a force on the rock, causing the rock to accelerate in the x-direction. According to Newton's third law, the rock exerts an equal and opposite force on the cart, which slows the cart down. This exchange results in the transfer of momentum from the cart to the rock.

What is the total momentum of the system after the rock is dropped into the moving railroad cart?

After the rock is dropped into the moving railroad cart, the total momentum of the system is still conserved. The total momentum before the event is the momentum of the cart (3000 kg·m/s), and the total momentum after the event is the combined momentum of the cart and the rock (2400 kg·m/s for the cart + 600 kg·m/s for the rock), which adds up to 3000 kg·m/s, the same as before.