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