The correct answer are E and C respectively. I just don\'t know how to get there

Question

The correct answer are E and C respectively. I just don't know how to get there.

Problem 3. Starting with the boxes shown below at rest on the ice surface of a skating rink, you push with a constant horizontal force on the upper of the two boxes. The top box does not slip on the bottom one. So, they move together across the ice. How much work does the lower box do on the top box as you push the boxes a distance d? 1n M+m M +m D) Fd M +m M+m Problem 4: A uniform density piece of plastic with dimensions 8cm× 8cm× 4cm floats in water when 3/4 submerged, as shown in the figure. What magnitude of force would you have to exert straight down on the block to submerge it completely? For this problem use the approximations g = 10 m/s, and pwater= 1 g/cm3 A) 2.56 N B) 1.92 N C) 0.64 N D) 0.32 N E) 0.08 N

Explanation / Answer

3) Both blocks are moving with same acceleration, a= F/(m+M)

Let the force exerted by lower block on upper block be f.

As f opposite to the direction of motion,

Net force on upper block, Fnet= F–f = m*a=m*F/(m+M)

or, f= M*F/(m+M)

Work done by f on upper block, W= –f*d = –M*F*d/(m+M)

4) As piece is in equilibrium, W= bouyant force

force required to submerge it completely is equal to buoyant force exerted on remaining volume.

F= volume*density*g

= 8*8*4*(1/4)*1*10–3*10 = 0.64 N

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