2 A block with mass m1 is placed on an inclined plane with s

[2.] A block with mass m1! is placed on an inclined plane with slope angle @ and is connected to a second hinging block with mass m2 >m1 by a massless cord passing over a small, frictionless pulley (see figure). The coefficient of kinetic friction between mass m1 and the incline is negligible. Find: a) the acceleration (vector) of mass m1; b) the acceleration (vector) of mass m2; c) the magnitude of the normal force on mass m1. d) the magnitude of the tension in the cord; Show your work. Write your results in terms of !, !, and g. Check the units/dimensions for each answer. Note: Depending on the method you use to solve this problem, the questions may be best completed in a different order. Hint: you may use different reference frames for the two masses (just clearly indicate them and be careful with the signs!)

Solution

acceleration of m1 = acceleration of m2 = a

force balance on m1 -> T - m1*gsin(@) = m1*a
force balance on m2 -> m2*g - T = m2*a
m2*g - m1*gsin(@) = a(m1 + m2)
a) a = g(m2 - m1sin(@))/(m1+m2) parralel to the plank, upwards
b) a = g(m2 - m1sin(@))/(m1+m2) downwards
c) N = m1*gcos(@)
d) T = m1*[g(m2 - m1sin(@))/(m1+m2)] + m1*gsin(@)