a laboratory experiment is set up as shown at the right. the three masses are 1k

Question

a laboratory experiment is set up as shown at the right. the three masses are 1kg, 2kg, and 3kg, respectively. The radius of gyration of m2 is 0.2m and friction is negligible. (a) what is the acceleration of the system? (b) what are the tensions T1 and T2? (c) Starting from rest, how long does it take the system to move 1m? (d) what is the final angular velocity of m3?

T, m2 5. A laboratory experiment is set up as shown at right. The three masses are 1 kg, 2 kg, and 3 kg, respectively. The radius of gyration of m2 is 0.2 m and friction is negligible. (a) What is the acceleration of the system? (b) What are the tensions 7i and T2? (c) Starting from rest, how long does it take the system to move 1 m? (d) What is the final angular velocity of m3? m1 T2 m3

Explanation / Answer

T1 = m1*a = a

m3*g - T2 = m3*a = 3a

T2 = 3g-3a

k = 0.2m

radius r = sqrt(2)*k = 1.414*0.2 = 0.2828 m

Net troque is (T2-T1)*r = I*(a/r)

(3g-3a-a)*0.2828*0.2828 = 2*0.2*0.2*(a)

2.35- 0.0799a = 0.08a

2.35 = 0.1599a

accelaration a = 2.35/0.1599 = 14.7 m/s^2

B) T1 = 14.7 N

T2 = 3g-3a = 3*9.81 - 3*14.7 = 14.67 N

C) u = 0 m/s

a = 14.7 m/s^2

S = 0.5*a*t^2

t = sqrt(2S/a) = Sqrt(2*1/14.7) = 0.368 S

d) alpha = a/r = 14.7/0.2828 = 51.98 rad/s^2

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