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Calculating magnitude of tension and acceleration

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Please see the attachment for the diagrams. Explain how to breakdown the problems.

12. A 2.6 kg mass, m2, on a 33.6 degree incline is connected to a 4.2 kg mass, m1, on a horizontal surface. The surfaces and the pulley are frictionless. If F = 31.9 N, what is the magnitude of the tension in the connecting cord?

13. Two masses of 4.75 kg each, connected by a string, slide down a ramp making an angle of 37 degrees with the horizontal. The coefficient of kinetic friction between M1 and the ramp is 0.31. The coefficient of kinetic friction between M2 and the ramp is 0.15. Find the magnitude of the acceleration of the masses.

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This solution is provided in 261 words. It provides step-by-step equations for finding tension and acceleration.

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1.) Let us assume the tension in the cord be T, and acceleration of the two blocks be a.

For block of mass m2, along the inclined plane,

F - T - m2*g*sin(theta) = m2*a ......(1)

For block of mass m1, along the horizontal plane,

T = m1*a .........(2)

Eqn. (1)*m1 - (2)*m2:

m1*F - T*m1 - m1*m2*g*sin(theta) - T*m2 = m1*m2*a - ...

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  • BEng, Allahabad University, India
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