Answer:
Explanation:
Given:
m1 = 17 kg
m2 = 10.5 kg
M = 5 kg
r = 0.3 m
Use the energy equation
Initial Energy = Final Energy
Initial Energy is only the potential energy of mass one (PE1).
Final Energy is the final kinetic energy of mass one (KE1), the final kinetic energy of mass two (KE2), the kinetic energy of the pulley (KEp) and the potential energy of mass two (PE2)
PE1 = KE1 + KE2 + KEp + PE2
PE1 = m1*g*h
PE2 = m2*g*h
KE1 = (1/2) m1 * v^2
KE2 = (1/2) m2 * v^2
KEp = (1/2) I w^2
I = (1/2) M r^2
w = (v/r)
PE1 = KE1 + KE2 + KEp + PE2
m1*g*h = (1/2) m1 * v^2 + (1/2) m2 * v^2 + (1/2) I w^2 + m2*g*h
Now substitute in I = (1/2) M r^2 and w = (v/r) inti the above equation, we have:
m1*g*h = (1/2) m1 * v^2 + (1/2) m2 * v^2 + (1/2) (1/2) M r^2 (v/r)^2 + m2*g*h
m1*g*h = (1/2) m1 * v^2 + (1/2) m2 * v^2 + (1/4) M v^2 + m2*g*h
m1*g*h - m2*g*h = v^2 [(1/2) m1 + (1/2) m2 + (1/4) M]
v^2 = (m1*g*h - m2*g*h)/[(1/2) m1 + (1/2) m2 + (1/4) M]
v^2 = g*h*(m1 - m2)/[(1/2) m1 + (1/2) m2 + (1/4) M]
v = sqrt[g*h*(m1 - m2)/[(1/2) m1 + (1/2) m2 + (1/4) M]]
Inputting values,
v = sqrt[9.81 * 4.40 *(17 - 10.5)/[(1/2) × 17 + (1/2) × 10.5 + (1/4) × 5]]
v = 4.325 m/s
There is one motion equation without acceleration
H = S + (1/2) * (vi - v0) * t
S = 0 m
v0 = 0 m/s
h = vi*t/2
t = 2 * H/vi
= 2 * 4.40/4.325
= 2.035 s.
