Question

# An object with mass m1 = 3.70 kg, rests on a frictionless horizontal table and is...

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

(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

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