two blocks of mass 4kg and 2kg are placed side by side on a smooth horizontal surface. A horizontal force of 20N is applied on 4kg block.
Find A) the acceleration of each block
B) normal reaction on the block B due to A
Answers
Answer:
Explanation:
m₁ = 4 kg
m₂ = 2 kg
Force applied = 20 N
Forces acting on 4 kg block are- Weight, Normal from ground, 20 N towards right and normal from 2 kg block towards left. (N₂)
Weight and Normal from ground will cancel each other as block is not accelerating up and down. So, Weight of 4kg block is equal to the normal by ground (40 N). The remaining forces are 20 N towards right and N₂ towards left, but the 4 kg block will accelerate towards right due to the horizontal force, and thus, 20 N > N₂
⇒ F(net) = F₁ - F₂ = m₁a
⇒ 20 - N₂ = (4) (a) ....... (i)
Now, forces acting on 2 kg block are - Weight, normal from ground and Normal from 4 kg block (N₄) towards right. [2 kg block don't know anything about the 20 N horizontal force because the force was not applied on it. It will experience only the Normal Force by 4 kg block which was applied on to it in the right direction, although this normal force is exerted on the 2 kg block due to the 20 N horizontal force only which was applied on the 4 kg block.]
So, the weight and Normal force by the ground of the 2kg block will cancel each other and it will only experience a force N₄ towards right.
⇒ F(net) = F₁ - F₂ = m₂a [Acceleration would be the same of both the blocks as no friction is there, think it practically]
⇒ N₄ - 0 = (2) (a)
⇒ N₄ = 2a ........ (ii)
Adding (i) and (ii),
20 - N₂ + N₄ = 6a [N₂ = N₄ by Newton's Third Law, so they will cancel each other]
20 = 6a
a = 10/3 m/s² (ANS.)
From (ii),
N₄ = 2a
= 2 × 10/3
= 20/3 N (ANS.)
So, Normal reaction between the two blocks is = 20/3 N.
IT WILL BE THE SAME ON BOTH THE BLOCKS.