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A block with mass m 1 ​ is placed on an inclined plane with slope angle α and is connected to a second hanging block with mass m 2 ​ by a cord passing over a small, frictionless pulley as shown in Fig. The coefficient of static friction is μ s ​ and the coefficient of kinetic friction is μ k ​ . a. Find the mass m 2 ​ for which block m 1 ​ moves up the plane at constant speed once it is set in motion. b. Find the mass m 2 ​ for which block m 1 ​ moves down the plane at constant speed once it is set in motion. c. For what range of values of m 2 ​ will the blocks remain at rest if they are released from rest?

User Timolawl
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Final answer:

In this physics question, we analyze a system with two blocks on an inclined plane and a pulley. By considering forces of gravity and friction, we can calculate for desired properties of the system such as the mass required for the blocks to stay at rest or move at a constant speed.

Step-by-step explanation:

The subject of this question is **physics**, focusing on the principles of motion, friction, and gravity. It involves analysing a system where two blocks, with masses m1 and m2, are connected via a cord over a frictionless pulley, with block m1 on an inclined plane.

To address part a, we consider block m1 moving up the plane at constant speed. The forces at play here are the gravity acting down the inclined plane (m1gsinα), the friction opposing the motion (μkm1gcosα, using the kinetic friction coefficient since the block is in motion), and the tension from the second block (m2g). Since the block is moving at a constant velocity, these forces balance out, resulting in the equation m1gsinα + μkm1gcosα = m2g. From this equation, you can solve for m2 to find the mass required for m1 to move up the incline at constant speed.

Part b is similar to part a, but in this case block m1 is moving downwards. This changes the directions of the forces, resulting in the equation m1gsinα - μkm1gcosα = m2g. Again, you can solve this equation for m2 to find the mass required for m1 to move down the incline at constant speed.

For part c, you need to find the range of m2 values for which the blocks will remain in static equilibrium. This involves setting the forces equal to each other considering both possibilities of block m1 being on the verge of moving up or down the incline. This will give two equations, and solving simultaneously will give the range of values for m2 where both blocks remain at rest.

Learn more about Friction and Gravity

User Laurie Young
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