Two blocks of masses m1 and m2 are placed on a table in contact with each other as shown in the figure below. The coefficient of kinetic friction between the block of mass m1 and the table is μ1, and that between the block of mass m2 and the table is μ2. A horizontal force of magnitude F is applied to the block of mass m1. We wish to find P, the magnitude of the contact force between the blocks.
(b) What is the net force on the system of two blocks? (Use any variable or symbol stated above along with the following as necessary: F, P, and g.)
Fnet = _F - (μ1*m1+ μ2*m2)*g_ N
(c) What is the net force acting on m1? (Use any variable or symbol stated above along with the following as necessary: F, P, and g.) Fnet,1= _F - (μ1*m1)*g - P_ N
(d) What is the net force acting on m2? (Use any variable or symbol stated above along with the following as necessary: F, P, and g.) Fnet,1=__F - (μ2*m2)*g + P_ N ---------------------- (1)
(f) Solve the two equations in two unknowns for the acceleration a of the blocks in terms of the masses, the applied force F, the coefficients of friction, and g. (Use any variable or symbol stated above along with the following as necessary: F.) a=_[{F/(m1+m2)} - {(μ1*m1+ μ2*m2)/(m1+m2)}*g]_ m/s^2 -----------(2)
(g) Find the magnitude P of the contact force between the blocks in terms of the same quantities. From (1) we get P=_Fnet,1 - F + (μ2*m2)*g _ N -------------------------------- (3) From (2), we get Fnet,1 = m1*[{F/(m1+m2)} - {(μ1*m1+ μ2*m2)/(m1+m2)}*g] -----------(4) Substituting (4) in (3) we get P = _m1*[{F/(m1+m2)} - {(μ1*m1+ μ2*m2)/(m1+m2)}*g] - F+(μ2*m2)*g_ or P = _[-{m2/(m1+m2)}F+(μ2*m2^2 - μ1*m1^2)*g]_ N
