can someone tell me how to solve this?

Question

A block of mass 7.33 kg lies on a frictionless
horizontal surface. The block is connected by
a cord passing over a pulley to another block
of mass 2.45 kg which hangs in the air, as
shown. Assume the cord to be light (massless
and weightless) and unstretchable and the
pulley to have no friction and no rotational
inertia.

Calculate the acceleration of the first block.
The acceleration of gravity is 9.8 m/s²
Answer in units of m/s²

Answer 1

Find the tension T in the cable, and use that to get the acceleration.

 

Block on horizontal surface:

 

M = 7.33 kg

 

(i)  T = Ma  [no friction, positive direction is direction of the tension, acceleration (a) is positive]

 

Hanging block:

 

m = 2.45 kg

 

T - mg = -ma  [positive up, negative down, same T by Newton's 3rd law, acceleration -a since down, same magnitude] ⇒

 

(ii)  T = m(g - a)

 

Plug this T into equation (i) and get

 

m(g - a) = Ma

 

Solve for a.

 

mg - ma = Ma

 

mg = (M + m)a

 

a = mg/(M + m) = (2.45)(9.8)/(7.33 + 2.45) m/s² ≅ 2.455 m/s²