Calculate the magnitude of the tension in the string

Question

a cart has a mass of 0.20kg and is attached by a rope in a pulley to a weight hanging off a table that weighs 0.4kg, assuming there is a frictional force of 0.10N, Calculate the magnitude of the tension in the string 

Answer 1

m =  mass of cart = 0.20 kg

M = mass of hanging weight = 0.40 kg [note 0.40 kg is the MASS, not the WEIGHT]

T = tension

f = friction = 0.10 N

a = acceleration of cart (+ toward pulley)

-a = acceleration of hanging mass (+ up, - down)

 

(i)   T - f = ma

(ii)  T - mg = -Ma

 

(ii) ⇒ a = (mg - T)/M

 

Plug a into (i).

 

T - f = m[(mg - T)/M] = (m/M)(mg - T)

 

Solve for T.

 

T - 0.10 = (0.20/0.40)[0.20(9.8) - T]

 

T - 0.10 = 0.98 - 0.5T

 

1.5T = 1.08

 

T = 0.72 N

 

You can also solve for a by plugging T into (i) or (ii), and get

 

a = 3.1 m/s²