Question

An object with mass m₁ = 3.70 kg, rests on a frictionless horizontal table and is connected to a cable that passes over a pulley and is then fastened to a hanging object with mass m₂ = 10.8 kg, as shown in the figure.

Two objects labeled m₁ and m₂ are attached together by a cable.

• Object m₁ lies on a horizontal table with the cable extending horizontally from its right side.
• The cable extends horizontally from the right side of m₁ then goes over a pulley and then straight down to m₂.
• Object m₂ hangs from the cable.

(a) Find the magnitude of the acceleration of each object.

a1=
a2=

(b) Find the tension in the cable.
N

Answer 1

(a)

The given two masses are connected by the same cable so they have the same acceleration:
The total mass of the system is

M = m1+m2

= 14.5 kg

The net force on the system is due to the force of gravity on the second hanging block.

Calculate the acceleration of the blocks by applying Newton' second law.

m2*g = M*a
a = 9.81*10.8/(14.5)

= 7.31 m/s2

a1=7.31 m/s2

a2=7.31 m/s2

(b)

Calculate the tension in the cable by applying Newton's second low on mass 2.

m2*g-T = m2a

T= m2*g-m2*a

= 9.81*10.8 - 10.8*7.31

= 27 N

Please “LIKE” the solution if this answer is helpful for you.

If you have any doubt please ask me in comment before rate.