Question

Two blocks are positioned on surfaces, each inclined at the same angle of 52.5 degrees with respect to the horizontal. The blocks are connected by a rope which rests on a frictionless pulley at the top of the inclines as shown, so the blocks can slide together. The mass of the black block is 5.05 kg, and the coefficient of kinetic friction for both blocks and inclines is 0.510. Assume static friction has been overcome and that everything can slide. What is must be the mass of the white block if both blocks are to slide to the LEFT at a constant velocity?

		2.21 kg
		11.54 kg
		5.05 kg
		8.30 kg

Answer 1

Inclined plane: movement and forces

Aswe know that, on an inclined plane the weight of an object decomposes into an x-component, parallel with the incline and a y-component, perpendicular on the incline. We marked them with x and y as usually, we choosing a Cartesian system of x-y axes along with those two directions.

If we mark the angle made by the incline with the horizontal with θθ and the weight of the object with G (from gravitational force which the Earth exerts on the object), then the relationship between these components and weight is:

In solving most of the problems involving an inclined plane, we use Newton's second law (expressing the relationship between force and acceleration):

Fnet=ma  ,where Fnet is the resultant of all the forces acting upon the object and the notion of tension in a string/rope/cord/cable/chain,etc. i.e. the force that appears in the string when pulled. This is a reaction force and, according to Newton's third law, is equal and opposite to the pulling force.

Solution:

We will start off by drawing diagrams showing the system of objects+inclined planes and the FBD for each object, for the above listed situation, in the text of the questions. Let us name the two objects A (for the white block) and B (for the black block).

To find: the mass of the white block if both blocks are to slide to the left at a constant velocity.