Question

Two objects (38.0 and 17.0 kg) are connected by a massless string that passes over a massless, frictionless pulley. The pulley hangs from the ceiling. Find (a) the acceleration of the objects and (b) the tension in the string.

Answer 1

Answer:

a) 3.7 m/s^2

b) 231.8 N

Explanation:

Let m1 be mass of the first object (m1 = 38.0 kg) and let m2 be the mass of the second object (m2 = 17.0 kg ). Let a be the acceleration of the two objects. Let F1 be the force of gravity exerted on m1 and F2 be the force of gravity exerted on m2. Let M = m1 +m2

a)

F1 = m1g and F2 = m2g

So Fnet = F1 + F2

Since the pulleys will move in different directions when accelerating...

Fnet = F1 - F2

M×a = m1g - mg2

M×a = g×(m1 -m2)

a = g×(m1 - m2)/M

a = 9.8×(38 - 17)/(38 + 17)

a = 3.7 m/s^2

b)

Looking at the part for m2

Fnet  = T - m2g

-m2×a = T - m2g

T = m2(g - a)

T = 231.8 N