hello can you please type steps with formulas and numbers? there are similar ans

Question

hello can you please type steps with formulas and numbers? there are similar answers on here but i dont understand where the numbers come from or what formulas they are using. thank you A mass m1 = 6.9 kg rests on a frictionless table. It is connected by a massless and frictionless pulley to a second mass m2 = 2.3 kg that hangs freely. the magnitude of the acceleration of block: 1m/s^2 the tension in the string: 16.905N Now the table is tilted at an angle of ? = 80.0? with respect to the vertical. Find the magnitude of the new acceleration of block 1: 1.17m/s^2 Now the table is tilted at an angle of ? = 80.0? with respect to the vertical. Find the magnitude of the new acceleration of block 1. *At what ?critical? angle will the blocks NOT accelerate at all *Now the angle is decreased past the ?critical? angle so the system accelerates in the opposite direction. If ? = 37.0? find the magnitude of the acceleration.

Explanation / Answer

A mass m1 = 6.9 kg rests on a frictionless table. It is connected by a massless and frictionless pulley to a second mass m2 = 2.3 kg that hangs freely.

The magnitude of the acceleration of block:

a = F/(m1+m2) = m2 g/(m1+m2) = 2.3*9.8/(2.3+6.9) = 2.45 2.5 m/s2

the tension in the string: T = m1 a = 6.9*2.45 = 17 N

Now the table is tilted at an angle of ? = 80.0° with respect to the vertical. Find the magnitude of the new acceleration of block 1:

a = F/(m1+m2) = (m2-m1cos80) g/(m1+m2) = (2.3-6.9*0.173648)*9.8/(2.3+6.9)

a 1.17 m/s^2

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

F = 0

===> m2 - m1cos = 0

===> m2 = m1cos

===> 2.3 = 6.9 * cos

===> cos =  2.3/6.9 = 0.333333

===> = cos-1(0.333333)

==> = 70.5 71 degrees

Now the angle is decreased past the “critical” angle so the system accelerates in the opposite direction. If ? = 37.0° find the magnitude of the acceleration.

a = F/(m1+m2) = (m1cos80-m2) g/(m1+m2)

a = (6.9*0.7986355 - 2.3)*9.8/(2.3+6.9)

a = 3.4 m/s2

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