Two Masses Connected Example Problem

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Two masses,

m1 = 2.26 kg and

m2 = 6.03 kg are

on a horizontal frictionless surface and they are

connected together with a rope as shown in the figure.

1. The rope will snap if the tension in it exceeds

75.0 N.

What is the maximum value of the force F which can be applied?

Given:

- m1 = 2.26 kg

- m2 = 6.03 kg

- T = 75.0 N

Need:

- max force in (N)

Equations:

- to find max force

max force = tension + (acceleration*m2)

- BUT we do not know acceleration so to find that, we use the equation:

acceleration = tension/m1

Work:

acceleration = tension/m1

a = 75.0N/2.26kg

a = 33.1858 m/s^2

Now plug the acceleration into the max force equation:

max force = T + a(m2)

F(max) = 75.0N + (33.1858*6.03kg)

F(max) = 275.2 N

2. What is the acceleration of the whole system, when this maximum

force is applied?

Equation:

acceleration = F(max)/(m1+m2)

a = 275.2N/(2.26kg+6.03kg)

a = 33.2 m/s^2