A 4 kg object hangs below a 6 kg object by a string of negligible mass. If the 6 kg object is pulled upward by a force of 440 N, what is the tension in the string?

176 N

Explanation:

Sum of the forces on the 6 kg object:

∑F = ma

F - Mg - T = Ma

Sum of the forces on the 4 kg object:

∑F = ma

T - mg = ma

Notice that since the objects are connected, they have the same acceleration.

Solving for acceleration in both equations:

a = (F - Mg - T) / M

a = (T - mg) / m

Set equal:

(F - Mg - T) / M = (T - mg) / m

Cross multiply and solve for T:

m (F - Mg - T) = M (T - mg)

mF - mMg - mT = MT - mMg

mF - mT = MT

mF = mT + MT

mF = (m + M) T

T = mF / (m + M)

Given F = 440 N, m = 4 kg, and M = 6 kg:

T = (4) (440) / (4 + 6)

T = 176 N