Question

In the figure here, a stationary block explodes into two pieces L and R that slide across a frictionless floor and then into regions with friction, where they stop. Piece L, with a mass of 2.5 kg, encounters a coefficient of kinetic friction μL = 0.43 and slides to a stop in distance dL = 0.38 m. Piece R encounters a coefficient of kinetic friction μR = 0.45 and slides to a stop in distance dR = 0.40 m. What was the mass of the block?

Answer 1

Given mass m_L =2.5kg and mass m_R = ?

= 0.43 and = 0.45

d_L = 0.38 m and d_R=0.4m

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During explosion momentum is conserved

so P_{before explosion} =P_{after explosion}

--------------------(1)

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Now consider body L

After explosion the body is coming to rest after traveling a distance d_L due to friction

Kinetic Energy = workdone by friction

Cancel m_L

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Similarly ,consider body R

After explosion the body is coming to rest after traveling a distance d_R due to friction

Kinetic Energy = workdone by friction

Cancel m_R

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Put v_L and v_R in equation (1)

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Mass of Block ,

ANSWER = 4.9kg

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