After a rockslide, three large boulders of mass m1 = 5.00 Times 102 kg, m2 = 7.0

Question

After a rockslide, three large boulders of mass m1 = 5.00 Times 102 kg, m2 = 7.00 Times 102 kg and m3 = 3.00 Times 102 kg block a busy highway through the mountains The rocks are side by side blocking the road and lined up from left to right in the order m}, m2, m3. A bulldozer is used to slide the rocks off the road; the bulldozer applies a constant force to the left side of m1. Assuming the rocks are all in contact and the road is a flat frictionless surface, what force, FA. must be applied to m1 to slowly accelerate the group of rocks from the road at 0.100 m/s2? Use the value found above for FA to find the force, F12, exerted by the first rock of mass 5.00 Times 107 kg on the middle rock of 7.00 Times 102 kg.

Explanation / Answer

The contact force between the m1 and m2 is T1 and that between the m2 and m3 is T2

For the first body

F -T1 =ma

For the second body T1-T2 =m2a

and for the third body T2 =m2a

Here F =(m1+m2+m3)a

a =F/(m1+m2+m3) ===>F =(m1+m2+m3)a =(5+7+3)*102kg*0.100m/s2 =150N

The force exerted by the first rock of mass 5.00*102kg on the middle rock is givenby

T12 =(m1+m2)F/(m1+m2+m3) =(5+7)*102*150/(5+7+3)*102 =1800/15=120N

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