Question

In the figure, a tin of anti-oxidants (m1 = 4.6 kg) on a frictionless inclined surface is connected to a tin of corned beef (m2 = 2.5 kg). The pulley is massless and frictionless. An upward force of magnitude F = 5.8 N acts on the corned beef tin, which has a downward acceleration of 5.8 m/s2. What are (a) the tension in the connecting cord and (b) angle β?

Answer 1

Weight of the tin of anti oxidants will act vertically downwards. Then dividing it into rectangular components with angle of inclination this tin as .

1st component: acting along the inclined surface towards the tin of corned beef,

  

2nd component: acting in perpendicular direction to the inclined surface,

(This component is balanced exactly by the normal reaction force on the tin by surface)

Now let Tension in the cord be "T" and since cord is same hence it will be same for both cords. Also the corned beef tin is moving downwards with acceleration,

a= 5.8m/s²

SInce the system is connected thus acceleration of anti-oxidant beef will be this only.

Considering the motion of anti-oxidant beef first, Using Newton's Laws of motion

Net Force on this tin,

Also we know that

thus we'll have

  .............................(1)

Now considering the motion of corned beef tin,

  (SInce force F acts on this tin in upward direction)

then using equation 1 in above,

  

Using all given values in above,

  

  

  

  

  (ANS)

Now using equation 1,

  

  (ANS)