Tipler6 9.P.076. The system shown below is released from rest. The m, 32 kg bloc

Question

Tipler6 9.P.076. The system shown below is released from rest. The m, 32 kg block is 2 m above the ledge. The pulley is a uniform disk with a radius of 10 cm and mass m 5 kg. Assume that the string does not slip on the pulley. (a) Find the speed of the 32 kg block just before it hits the ledge You currently have 0 submissions for this question. Only 2 submission are allowed. You can make 2 more submissions for this question. (b) Find the angular speed of the pulley at that time rad/s Subm You currently have 0 submissions for this question. Only 2 submission are allowed. You can make 2 more submissions for this question. (c) Find the tensions in the strings N (left) You currently have 0 submissions for this question. Only 2 submission are allowed. You can make 2 more submissions for this question. N (right) s You currently have 0 submissions for this question. Only 2 submission are allowed. You can make 2 more submissions for this question. (d) Find the time it takes for the 32 kg block to reach the ledge

Explanation / Answer

(A) Applying energy conservation,

PEi + KEi = PEf + KEf

32 g h + 0 = 20 g h + ((32 + 20)v^2 /2 + I w^2 / 2)

g h (32 - 20) = 52 v^2 /2 + (5 r^2 /2)(v/r)^2 /2

9.8 x 2 x 12 = 26 v^2 + 2.5 v^2

v = 2.87 m/s ........Ans

(B) w = v / r = 2.87 / 0.10 = 28.7 rad/s ........Ans

(C) vf^2 - vi^2 = 2 ad

2.87^2 - 0^2 = 2 (a)(2)

a = 2.06 m/s^2

left string: T - 20g = 20 a

T = 20(9.8 + 2.06) = 237.3 N  

Right string: 32g - T =32 a

T = 247.7 N  

(D) 2.87 = 0 + 2.06 t

t = 1.39 sec

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