A mass m 1 = 6.8 kg rests on a frictionless table. It is connected by a massless

Question

A mass m1 = 6.8 kg rests on a frictionless table. It is connected by a massless and frictionless pulley to a second mass m2 = 2.2 kg that hangs freely.

1-Now the table is tilted at an angle of = 80° with respect to the vertical. Find the magnitude of the new acceleration of block

2- At what “critical” angle will the blocks NOT accelerate at all?

3- Now the angle is decreased past the “critical” angle so the system accelerates in the opposite direction. If = 35° find the magnitude of the acceleration.

also i have another question:

A tennis ball connected to a string is spun around in a vertical, circular path at a uniform speed. The ball has a mass m = 0.177 kg and moves at v = 4.64 m/s. The circular path has a radius of R = 0.88 m

4) What is the minimum velocity so the string will not go slack as the ball moves around the circle?

i tried to solve them but didn't work :(

Explanation / Answer

multiple questions I am allowed to solve only 1 question at a time .

part 1)
a = (m2g - m1gsin140)/(m1+m2)

part 2)
a = m2g - m1gsinx/(m1+m2) = 0 -->
m2g = m1gsinx
x = sin^-1 (m2g/m1g) (with x = angle with horizontal)
x = sin^-1(m2/m1)
angle with vertical = 90-x

part 3)
F = m1gsin35 - m2g
a = (m1gsin35 - m2g)/(m1+m2)

so you just need to plug the value of m1 and m2 to find the soln to the problem.

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