# Momentum Conserved? Physics Q&A on 1 kg Cart

• jeffxtreme
In summary, the conversation discusses the concept of conservation of momentum in the context of a physics question involving a cart and a weight being dropped onto it. The initial momentum of the cart is calculated to be 5 kg m/s and if momentum were conserved, the final velocity would be 2.5 m/s. However, there is confusion about how the cart can be decelerated to this velocity without an external force. The concept of inelastic collisions is explained, where the impulse of the collision is equal to the change in momentum. It is also noted that the duration of the collision is important in determining the force and potential injuries in real-life scenarios. Finally, it is clarified that if the weight is first accelerated to the same speed
jeffxtreme

Assume for example a 1 kg cart is moving at a constant speed of 5 m/s on a frictionless service. Then, a 1 kg weight is dropped onto the cart. Would its initial momentum be conserved? What would be it's final velocity?

At first, the cart has a momentum of 5 kg m /s. If momentum were conserved, its final velocity would be 2.5 m/s. However, I do not really understand this. According to Newton's First Law of Motion, an object will remain in equilibrium unless acted on by an external force. The cart is apparently instantaneously decelerated to 2.5 m/s. How is this possible? What is the external force applied on the cart?

If the cart remained the same velocity (5 m/s before and after the weight was added), then conservation of momentum wouldn't hold.

Any help and insight would be greatly appreciated. It might just be that I don't really understand the laws of motion and momentum. Thanks in advance.

You would view this as an inelastic collision. Yes, momentum is conserved. The collision will occur over some amount of time giving you what's called an impulse. force = momentum/time. So, the force between the box and cart acts over some delta time. Equal and opposite means force on box and cart is the same. Since both forces act over the same amount of time, box and cart change momentum by the same amount. force*(delta time) = delta momentum. All we see though is the delta momentum. The specific force and time are unknown in general, and are specific to the properties of the two objects and how they interact (ie large force/small time, small force large time). However, it is important for things like car crashes. If the impact time is small, that means the force is large, which means the people inside the car (or the cart) will probably die. This gives you ways to engineer objects so collisions are "safe".

Oh, okay, thanks Longstreet, now I understand. If we assume that the weight is set (not thrown) on the cart, we could say that there is an inelastic collision occurring with the initial velocity of the weight being negligibly small (giving it a negligibly small initial momentum).

Pi = Pf
Pci + Pwi = P(c+w)f
(1 kg)(5 m/s) + 0 = (x m/s)(2 kg)
x = 2.5 m/s

It also makes sense force-wise, the cart is putting force on the weight, speeding the weight up. Meanwhile, the weight is putting an equal and opposite force on the cart, slowing the cart down.

However, if we hadn't set the weight down on the cart, but rather first accelerated it to the same speed as the cart and then set it down, it wouldn't change the final velocity.

Again, thanks for clearing that up.

Last edited:

## 1. What is momentum conservation?

Momentum conservation is a fundamental principle in physics that states that the total momentum of a closed system remains constant. This means that the total amount of motion in a system does not change unless an external force is applied.

## 2. How is momentum conserved?

Momentum is conserved through interactions between objects in a system. When two objects collide, they exert equal and opposite forces on each other, resulting in a transfer of momentum. As long as there are no external forces acting on the system, the total momentum remains constant.

## 3. What is the equation for momentum conservation?

The equation for momentum conservation is pi = pf, where pi is the initial momentum of the system and pf is the final momentum of the system. This equation represents the principle that the total momentum before an interaction is equal to the total momentum after the interaction.

## 4. What is the role of mass in momentum conservation?

Mass plays a crucial role in momentum conservation because momentum is defined as the product of an object's mass and velocity. In a closed system, the total mass remains constant, so any changes in momentum must be due to changes in velocity.

## 5. How does momentum conservation apply to a 1 kg cart?

If a 1 kg cart is the only object in a closed system, its momentum will remain constant unless acted upon by an external force. This means that if the cart is moving at a constant velocity, it will continue to do so unless an external force, such as friction or a collision, changes its momentum.

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