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Block 1 of mass 2 m is connected to Block 2 of mass m using an inextensible rope and pulley of negligible mass as shown in the diagram below. The coefficient of kinetic friction between Block 1 and the inclined plane is μ1 whereas that between Block 2 and the inclined plane is μ2. It is observed that Block 1 accelerates down the incline pulling Block 2 up the incline. (a) Derive an expression for the acceleration of the system, a in terms of the given variables only m, μ1, μ2 and any constants, such as g. (b) Calculate the tension in the string given m = 3.0 kg, θ1 = 60∘, θ2 = 30∘, μ1 = 0.2, μ2 = 0.4 (c) If the inclined planes are frictionless, what is the acceleration of the system? Hint: Modify the expression you derived in part (a) to obtain an expression for the acceleration of the system in this case.

Block 1 of mass 2 m is connected to Block 2 of mass m using an inextensible rope and pulley of negligible mass as shown in the diagram below. The coefficient of kinetic friction between Block 1 and the inclined plane is μ1 whereas that between Block 2 and the inclined plane is μ2. It is observed that Block 1 accelerates down the incline pulling Block 2 up the incline. (a) Derive an expression for the acceleration of the system, a in terms of the given variables only m, μ1, μ2 and any constants, such as g. (b) Calculate the tension in the string given m = 3.0 kg, θ1 = 60∘, θ2 = 30∘, μ1 = 0.2, μ2 = 0.4 (c) If the inclined planes are frictionless, what is the acceleration of the system? Hint: Modify the expression you derived in part (a) to obtain an expression for the acceleration of the system in this case.

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Block 1 of mass 2 m is connected to Block 2 of mass m using an inextensible rope and pulley of negligible mass as shown in the diagram below. The coefficient of kinetic friction between Block 1 and the inclined plane is μ 1 whereas that between Block 2 and the inclined plane is μ 2 .
It is observed that Block 1 accelerates down the incline pulling Block 2 up the incline. (a) Derive an expression for the acceleration of the system, a in terms of the given variables only m , μ 1 , μ 2 and any constants, such as g . (b) Calculate the tension in the string given m = 3.0 k g , θ 1 = 60 ∘ , θ 2 = 30 ∘ , μ 1 = 0.2 , μ 2 = 0.4 (c) If the inclined planes are frictionless, what is the acceleration of the system? Hint: Modify the expression you derived in part (a) to obtain an expression for the acceleration of the system in this case.

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