The block in the diagram below is at rest. however, the tension in the cable is not the only thing holding the block back. static friction is also applying a force. if the coefficient of static friction is 0.214 determine the
tension in the rope.

The  tension in the rope is 229.37 N.

Explanation:

Given:

Mass of the block is,

Coefficient of static friction is,

Angle of inclination is, °

Draw a free body diagram of the block.

From the free body diagram, consider the forces in the vertical direction perpendicular to inclined plane.

Forces acting are and normal . Now, there is no motion in the direction perpendicular to the inclined plane. So,

Consider the direction along the inclined plane.

The forces acting along the plane are and frictional force, , down the plane and tension, , up the plane.

Now, as the block is at rest, so net force along the plane is also zero.

Therefore, the  tension in the rope is 229.37 N.

0.11 m/s and 0.28 m/s should be correct