How Does Mass and Velocity Affect Momentum on a Moving Conveyor Belt?

[bc33rocks]

1.Sand from a stationary hopper falls on a mov-
ing conveyor belt at the rate of 4 kg/s, as
shown in the figure. The belt is supported by
frictionless rollers and moves at 1.07 m/s un-
der the action of a horizontal external force
supplied by the motor that drives the belt.
Find the sand’s rate of change of momen-
tum in the horizontal direction. Answer in
units of N.



2. i know the rate of change of momentum is equal to the force but i need help figuring out that i really just need help getting started



3.

 

[LowlyPion]

1.Sand from a stationary hopper falls on a mov-
ing conveyor belt at the rate of 4 kg/s, as
shown in the figure. The belt is supported by
frictionless rollers and moves at 1.07 m/s un-
der the action of a horizontal external force
supplied by the motor that drives the belt.
Find the sand’s rate of change of momen-
tum in the horizontal direction. Answer in
units of N.

2. i know the rate of change of momentum is equal to the force but i need help figuring out that i really just need help getting started
3.

Welcome to PF.

Well what is the change in momentum?

Momentum after - momentum before? I can't see your picture, but I suppose it falls vertically. So the final speed in X is what? The initial speed in X is what and what is the rate of sand mass in 1 sec? ...

 

[nlightner]

Hello,

I can help you with this problem. First, let's define some variables to make it easier to understand. Let's say that the mass of the sand is m and the velocity of the conveyor belt is v. We can also define the change in time as Δt.

Now, we know that the rate of change of momentum is equal to the force, as stated in the problem. This can be written as:

Rate of change of momentum = Force

In this case, the force is the external force supplied by the motor that drives the belt. We can represent this force as F.

So, the equation becomes:

Rate of change of momentum = F

But we also know that momentum is equal to mass multiplied by velocity (p = mv). So, we can rewrite the equation as:

Rate of change of momentum = mΔv/Δt

Where Δv is the change in velocity, which in this case is the velocity of the sand, and Δt is the change in time.

Now, we need to find the value of mΔv/Δt. We know that the mass of the sand is 4 kg/s and the velocity of the conveyor belt is 1.07 m/s. So, the change in velocity would be 1.07 m/s and the change in time would be 1 second.

Therefore, mΔv/Δt = (4 kg/s)(1.07 m/s)/1 s = 4.28 kgm/s^2 = 4.28 N

So, the rate of change of momentum in the horizontal direction is 4.28 N.

I hope this helps you get started with solving this problem. Let me know if you have any further questions.