Posted by emm on .
Two blocks are connected by a string over a frictionless, massless pulley such that one is resting on an inclined plane and the other is hanging over the top edge of the plane. the hanging block has a mass of 16 kg and the one on the plane has a mass of 8 kg. the coefficient of kinetic friction between the block and the inclined plane is 0.23. the blocks are released from rest.
a. what is the acceleration of the blocks?
b. what is the tension in the string connecting the blocks?
(I want to check my answers.. I got an acceleration of 4 m/s2, and for tension I'm not sure, I got a tension above the hanging block to be 92.8 ?)
The answer will depends upon the incline angle of the plane, which you did not provide.
Write free body F = ma equations for both blocks. The string tension T will appear in both equations. The other unknown will be the acceleration, a. You should be able to solve for both.
Also the angle of the plane is at 37 degrees
The friction force acting on the sliding mass is
8*9.8*cos37*0.23 = 14.4 N
A gravity componet of M g sin 37 = 47.2 also acts on the slid9ing block.
Equations of motion are:
T - 14.4 - 47.2 = T - 61.6 = 8 a
16 g - T = 156.8 - T = 16 a
Note that the same tension force operates on both blocks, but in opposite directions (forward and back).
Eliminate T first
95.2 = 24 a
a = 3.97 m/s^2
T = 61.6 + 8a = 93.3 N
Our answers very nearly agree. The differences may be in how we rounded numbers along the way.