- #31
Tanya Sharma
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Satvik Pandey said:
I am glad you were able to solve the problem
Mechanics problem -- 2 masses & spring on a surface
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SUMMARY
The forum discussion focuses on calculating the minimum force required to move mass M2, given M1=3kg, M2=5kg, and coefficients of friction μ1=0.4 and μ2=0.6. The initial approach using Newton's laws and the spring force kx was deemed incorrect because it did not account for the transition from static to kinetic friction. The correct method involves applying the work-energy theorem, leading to the conclusion that the minimum force F must equal g(μ1M1 + μ2M2/2) when the velocity of block 1 is zero, ensuring block 2 begins to move.
PREREQUISITES- Understanding of Newton's laws of motion
- Knowledge of friction coefficients (static and kinetic)
- Familiarity with the work-energy theorem
- Basic concepts of spring mechanics and force constants
- Study the work-energy theorem in detail, focusing on its application in mechanics problems.
- Learn about the differences between static and kinetic friction and their implications in motion.
- Explore spring mechanics, specifically Hooke's law and the behavior of springs under varying forces.
- Practice solving problems involving multiple masses and forces on surfaces to solidify understanding of equilibrium and motion.
Students studying physics, particularly those focusing on mechanics, as well as educators and tutors seeking to clarify concepts related to forces, motion, and energy in systems involving multiple masses and springs.
I am glad you were able to solve the problem
- #32
ehild
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Satvik Pandey said:
Your approach assumed that both masses are moving. Only in that case are the forces of friction μmg. If one of the mass is in rest, friction is static. Can be less than μmg.
The masses in the problem can move in a peculiar way. Initially both are in rest, so the force F has to overcome μ1m1g and the elastic force of the spring. But the other mass is in rest, till the elastic force overcomes the frictional force acting to it. At the same time, the first mass can get into rest, and the elastic force alone drives the second mass forward. So the average applied force can be less than μ1m1g+μ2m2g.
ehild