Question

In: Physics

When vertically falling sand lands in a horizontally moving cart, the cart slows. Ignoring friction, give...

When vertically falling sand lands in a horizontally moving cart, the cart slows. Ignoring friction, give two reasons for this, one in terms of a horizontal force acting on the cart and one in terms of momentum conservation.

b) In a movie, the hero jumps straight down from a bridge onto a small boat that continues to move forward with no change in velocity. What physics is being violated here?

Solutions

Expert Solution

Let the weight of cart = mc Kg
Let the speed of Cart = Vc i^
Let the mass of sand = ms Kg

For a collision occurring between object 1 and object 2 in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision. That is, the momentum lost by object 1 is equal to the momentum gained by object 2.

Now, As the Cart is moving Horizontally it has Velocity in Horizontal Direction.
But the Sand is falling vertically.

After Falling down, both the Cart & Sand has Velocity in the Horizontal Direction, let us say = v.

Using Momentum Conservation -
mc * vc = (mc + ms) * v
v = [mc/(mc + ms)] * vc

This clearly proves, Velocity decreases and Cart Slows down.

We know,
Force = Mass * Acceleration

If sand is added into the Cart, Mass of the Cart increases, but Force remains the same, thus it Decreases the Acceleration of the Cart and it starts slowing down.

(b)
Newton's Law of motion is being Violated.
Momentume is not Conserved.


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