Two blocks are tied together with a string as shown in the diagram.(There is a block on a horizontal incline, its mass is 1.0kg, there is a rope connecting that block to a pulley which then connects to another block that is 2.0kg. The angle of the incline is 30 degrees) If both the pulley and the incline are frictionless, what is the acceleration of the 1.0kg block up the incline?
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The acceleration of the 1.0kg block up the incline is 1.73 m/s^2. This can be calculated using the equation a = (T - mgsinθ)/m, where T is the tension in the rope, m is the mass of the block, g is the acceleration due to gravity, and θ is the angle of the incline. In this case, T = 2.0kg * 9.8m/s^2 = 19.6N, m = 1.0kg, g = 9.8m/s^2, and θ = 30 degrees. Plugging these values into the equation gives a = (19.6N - (1.0kg * 9.8m/s^2 * sin(30))/1.0kg = 1.73 m/s^2.
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