A 2.00 kg object A is connected with a massless string across a massless, fricti

Question

A 2.00 kg object A is connected with a massless string across a massless, frictionless pulley to a 3.00 kg object B. The smaller object rests on an inclined plane which is tilted at an angle 40 degrees as shown. What are the acceleration of the system and the tension in the string?

The answers are a= 3.36 m/s^2 and T=19.3N

A 2.00 kg object A is connected with a massless string across a massless, frictionless pulley to a 3.00 kg object B (Figure 4-41). The smaller object rests on an inclined plane which is tilted at an angle of theta = 40.0 degrees as shown. What are the acceleration of the system and the tension in the string?

Explanation / Answer

let the tension be T

let the acceleration be a.

Force balance on A block

T - ma Sin(40) * g = ma * a _________________eq1

Force balance on B block

mb g - T = mb * a_____________________eq 2

Put the value of T from eq 1 in 2

mb *g  - ma Sin(40) *g - ma * a  = mb * a

3 *9.81 - 2* 0.643 * 9.81 = 5 a

a = 3.363 m/s2

T = ma Sin(40) * g + ma * a

T = 2* 0.643 * 9.81 + 2 * 3.363

T = 19.34 N

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