Answer to Question #118991 in Classical Mechanics for emosi

Question

In the system shown, a horizontal force Fx = 40 N acts on an object of mass m2 = 8.00 kg. A friction force fk = 5 N acts between object m2 and the table top, and m1 = 2.00 kg. i) Calculate the acceleration of the masses. ii) Calculate the tension in the string.

Answer 1

Given,

The masses $m_1=2Kg,m_2=8Kg$ and frictional force acting between table and those masses is $f=f_k=5N$ .

Horizontal external force is $F_x=40N$ acting on object of mass $m_2$ and also both masses are connected by string.

Now, lets draw the Free Body Diagram(FBD) for the system.

i). Now applying Newton's second law we get

$$F_{net}=m_{total}\cdot a_{net}\\ \implies (F_x-f_k)=(m_1+m_2)a_{net}\\ \implies 40-5=(2+8)a_{net}\implies a_{net}=3.5m/s^2$$

Thus, acceleration of each mass is $3.5m/s^2$ .

ii). Let $T$ denotes the tension force.

Now,consider the FBD object of mass $m_1$

Clearly, from the above diagram we get,

$$T-f_k=m_1a_{net}\\ \implies T=f_k+m_1a_{net}\implies T=5+2\times3.5=12N$$

Thus, Tension on the string is $12N$ .