1D dynamics MRPS multisystem (Ramp)

Question

A block (m1 = 6.8 kg) is being pulled up a ramp (at an angle = 27.4 degrees from the horizontal) with a cable that is parallel to the ramp's surface. The cable runs over a pulley that is at the top of the ramp and then is attached to a hanging block (m2 = 14.7 kg). What is the tension in the cable? Assume that the coefficient of kinetic friction for the block on the ramp is 0.5.

Answer 1

The standard way to solve this Atwoods problem is to do a force balance on each object assuming the "+direction" is down for the hanging mass and up the hill for the mass on the incline.

The Force balance on the mass on the incline (let's call it m₂) is T - m₂gsinθ - m₂gcosθ = m₂a

The Force balance on the hanging mass(m₁) is m₁g - T = m₁a

Add these two equations and solve for a which is the same for the attached masses.

In order to find T, substitute the a that you find into the hanging mass force balance and solve for T.

Good luck!