Question

A horizontal force of 500 N pulls two masses of 10 and 20 kg lying on a frictionless table connected by a light string. What is the tension in the string and acceleration of the system.

Answer 1

500-t =10a

t=20a

substitute the below equation in the above one

500=30a

a=50/3 ,now substitute the above value in first equation to get tension

t=100/3

Answer 2

By using Newton's second law

for 10 kg,

    $F = ma$

     $T = 10a$------ (1)

for 20 kg,

      $F = ma$

     $500 - T = 20a$----- (2)

• Substituting equation (1) to equation (2),

     $500 - 10a = 20a$

     $30a = 500$

     $a = 50/3 =16.67 m/s^{2}$

     acceleration of the system = 16.67 m/s²

• Substituting acceleration(a = 16.67) value for equation (1),
•      $T = 10* 16.67$    
•     $T = 166.7 N$
• tension of the string = 166.7 N