# Calculating Impulse and Momentum for a Dump Truck

• ludakrishna

#### ludakrishna

1. A dump truck is being filled with sand. The sand falls straight
downward from rest from a height of 2.00 m above the truck bed, and the
mass of sand that hits the truck per second is 55.0 kg/s. The truck is
parked on the platform of a weight scale by how much does the scale
reading exceed the weight of the truck and sand?

2. J = Ft p=mv mv(f) - mv(0)

3. i am completely lost.

The relevant equation is "force = rate of change of momentum".

Start by finding the momentum of the sand just before it hits the truck.

Mass per second = 55kg , h= 2m

because mgh = ½ mv2

Velocity of sand v=sqrt(2gh) , = 6.2 m/s

I am going round and round.

When sand hits the top of the truck it hits it with a force which is equal to change in momentum. Final velocity of sand is 6.2 m/s which becomes zero upon striking the truck.

This change in momentum gives the force that cause apparent increase in weight.

V1= 6.2 , V2= 0

F = m a = (m V1- mV2) = 55 x 6.2 = 341 Newton

Mass = weight/g = 341/9.81 = 34.7 kg

i'm stuck from here on

This change in momentum gives the force that cause apparent increase in weight.
V1= 6.2 , V2= 0

F = m a = (m V1- mV2) = 55 x 6.2 = 341 Newton

Mass = weight/g = 341/9.81 = 34.7 kg

i'm stuck from here on

Right. So why are you setting it equal to ma?? Weight is measured in Newtons, not kilograms.

You got it. The answer to the question is 341 Newton, or 34.7 kgF.

Most likely the truck will be on a scale calibrated in "Kilograms" which means kilograms force not kilograms mass.

1 kgF = the force exerted by the Earth's gravity on a mass of 1 kg = 9.81 Newtons.