7 . 1. A frictionless table is tilted at angle of = 30° with respect to the vert

Question

7 . 1. A frictionless table is tilted at angle of = 30° with respect to the vertical as show in Fig. Ablock of mass m 24.0 kg/tests on thetable. It is connected by a massless pulley to a ball of mass m2 5.00 kg that hangs freely. If al frictional forces of the table and pulley may be neglected, what is the magnitude of the acceleration of the m2 block2 (7 pt) (A) 3.248 m/s2 (B) 2.366 m/s (C) 1.960 m/s* (D) 1.856 m/s2 (E) 1.704 m/s' Fig. 7 main Ga 00(a (m2) 2n0 (4.1)sin 30 m2 CY 12. Continuing from the previous question, if the angle of the table can be adjusted, at a critical angle 0cr the blocks will not accelerate. What is this critical angle ecr? (7 pts) (A) 18.75° (B) 16.13° (C) 12.02° (D) 15.66" (E) 14.48

Explanation / Answer

we have from the newtons second law

F = ma

the accleration of the block 1 and block 2 is same and is given by

a = Fnet/(m1+m2)
where Fnet = (m2g - m1*g*sin30)

substituing the given valus, we get
a = (5*9.81 - 24*9.81*sin30)/29 = -2.368 m/s2

to find the critical angle for which there is no accleration, we have
m2*g = m1*g*sin(x)
or sin(x) = m2g/(m1g)
sin(x) = 5/24 = 0.208
x = 12.005° ( with the horizontal)  

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