An overnight rainstorm has caused a major roadblock. Three massive rocks of mass

Question

An overnight rainstorm has caused a major roadblock. Three massive rocks of mass m1 = 5.00 × 102 kg, m2 = 723 kg and m3 = 366 kg have blocked a busy road. The rocks are side by side blocking the road and lined up from left to right in order as m1, m2 and m3. The city calls a local contractor to use a bulldozer to clear the road. The bulldozer applies a constant force to m1 to slide the rocks off the road. Assuming the road is a flat frictionless surface and the rocks are all in contact, what force, FA, must be applied to m1 to slowly accelerate the group of rocks from the road at 0.400 m/s2?
Use the value found above for FA to find the force, F12, exerted by the first rock of mass 5.00 × 102 kg on the middle rock of 723 kg. Use Newton's Second (F = ma) and Third Law (action and reaction) to find the force needed to accelerate the system of rocks from the road.

Explanation / Answer

Combined mass = 1599kg
Acceleration = 0.4 m/s2

Force = ma = 639.6N

Force exerted by rock one on rock two:

mass=510kg

a=0.4 m/s2

F = 204N

Force applied directly = 639.6N

F12, exerted by the first rock of mass 5.00 × 102 kg on the middle rock of 723 kg = 435.6N

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