**15. ssm 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?

 

So as sand falls to the bed of the truck, the truck bed exerts a force upward to bring the sand to rest from the velocity the sand has as it hits the truck.  This net force up is the amount of force the scale reports above the actual weight of the truck. 

 

 

This impulse force then is what changes the momentum of the sand from moving to being at rest.

Since final velocity is zero after impacting truck.  Moreover, since F is pointing up and we will consider that positive, the initial velocity is pointing down which must be negative,  must therefore be positive and point up.  So we can now drop vector signs.

 

 

To find  we use conservation of mechanically energy.  Assume the sand falls from rest at the height of 2.00 m.  Therefore we have initially all gravitational potential energy and just before the bed of the truck it is all kinetic energy.

 

 

 

 

 

 

 

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This page last updated on January 11, 2020