Question

Two blocks with different mass are attached to either end of a light rope that passes over a light, frictionless pulley that is suspended from the ceiling. The masses are released from rest, and the more massive one starts to descend. After this block has descended a distance 1.30 m, its speed is 3.00 m/s.
A) If the total mass of the two blocks is 17.0 kg, what is the mass of the more massive block?Take free fall acceleration to be 9.80 m/s^2. (mass 1)
B) What is the mass of the lighter block?
Take free fall acceleration to be 9.80 m/s^2. (mass 2)

Answer 1

Answer:

(A) M2 = 11.5 kg

(B) M1 = 5.5 kg

Explanation:

distance (h) = 1.3 m

speed (u) = 3 m/s

free fall acceleration (g) = 9.80 m/s^2

total masses (M1 + M2) = 17 kg  .....equation 1

(A) from the conservation of energy, change in kinetic energy (KE) = change in potential energy (PE)

ΔKE = ΔPE

0.5$v^{2}$(M1) - (-0.5$v^{2}$(M2)) = gh ( M2 - M1)  

0.5$v^{2}$(M1 + M2) = gh ( M2 - M1)  

substituting all required detail in the equation above we have

0.5 x (3 x 3) x (17) = (9.8 x 1.3) x (M2 - M1)

76.5 = 12.74 x {M2 - M1)

(M2 - M1) = 76.5 / 12.74

M2 - M1 =6 kg ....equation 2

recall that the total mass : (M1 + M2) = 17 kg  ... equation 1

we can solve the two equations above simultaneously by adding the two equations together

M1 + M2 = 17 kg  ... equation 1

M2 - M1 = 6 kg ....equation 2

M1 + (-M1) + M2 + M2 = 17 + 6

2(M2) = 23

M2 = 11.5 kg

substituting the value to M2 into equation 1 we have

M1 + M2 = 17 kg  ... equation 1

M1 + 11.5 = 17

M1 = 17 - 11.5 = 5.5 kg

M1 = 5.5 kg