Newton's Laws of Motion

Q. Newton's Laws of Motion

Question
1)
A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m by applying a force P at one end of the horizontal  rope. Find the force which the rope exerts on the block.
2) 
Two masses m1 & m2 are connected by a light string passing over a smooth pulley.When set free m1 moves downwards by 1.4m in 2s.Then find the ratio of m1/m2. (g=9.8m/s^2).
3)
State(with reason) whether the following statements are true or false:
A) Action equals reaction only if the bodies are not accelerating.
B) It is easier to push than to pull a lawn roller. 
  
Answer

1) 
Treating block and rope as a system,
P = (m +M)a ... (1)
If  F = force applied on the block, then 
F = Ma ... (2)

(2) divided by (1)
=> F/P = M/(m+M)
=> F = PM/(m+M)

2)
Let T = tension in the string. Pulley is assumed to be of negligible mass.
=> m1g - T = m1a 
and T - m2g = m2a

Adding,
(m1 -m2)g = (m1 + m2)a
=> (m1 - m2)/m1 + m2) = a/g
=> m1/m2 = (g + a)/(g - a) ... (1)

For the motion of mass m1 and m2,
1.4 = (1/2)a(2)^2
=> a = 0.7 m/s^2

Plugging this value of a in (1),
m1/m2 
= (9.8 + 0.7)/(9.8 - 0.7)
= (10.5)/(9.1) 
= 15/13.

A) 
False. Newton's third law of motion is valid for bodies in contact even if they are accelerating.
 B) 
False. It is easier to pull rather than push. While pushing, the vertical component of the applied force is downwards and adds up to weight which increases the normal reaction from the ground and hence the frictional force. While, pulling, the vertical component of the applied force is upwards and gets subtracted from weight thus reducing the normal reaction from the ground and hence decreasing the friction.