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A 10 kg mass on a horizontal friction free air track is accelerated by a string attached to another 10-kg mass hanging vertically from a pulley as shown.What is the force due to gravity in newtons of the hanging 10-kg mass? What is the acceleration of the system of both masses?

Verified Answer :

HomertheGenius

1 ) The force due to gravity:
F g = m g = 10 kg 9.81 m/s² 
F g = 98.1 N
2 ) The system:
m 1 a = m g - T
+
m 2 a = T 
-----------------------
a (m 1 + m 2) = m g
a * 20 kg = 98.1 N
a = 98.1 : 20
a = 4.905 m/s²

1. Answer;

Force = 98.1 Newtons

Explanation;

-On the hanging mass the net force is

Fnet = Mhg - T = Mha where Mh is the mass = 10kg, g = 9.81m/s², and T the tension in the string. Its acceleration is a ( same as g)

Thus; Force = 10 kg × 9.81 m/s²

= 98.1 Newtons.

2. Answer;

a = 4.905 m/s²

Solution;

-We know that that T = Msa, but Fnet = Mhg - T = Mha

Substituting; T with Msa

Mhg - Msa = Mha

Mha + Msa = Mhg

a = Mhg/(Mh + Ms)

= 10.0kg9.81 m/s²/(10kg + 10kg)

= 4.905 m/s²

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