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A 4-kg block and a 2-kg block can move on the horizontal frictionless surface. The blocks are accelerated by a+12-N force that pushes the larger block against the smaller one. Determine the force that the 2-kg block exerts on the 4-kg block.
A) -4 N
B) -12 N
C) 0 N
D) +4 N
E) +8 N

Answer :

Answer:

[tex]F_n = -4 N[/tex]

Explanation:

Net external force that exerted on the block is given as

[tex]F_{net} = (m_1 + m_2) a[/tex]

here we know that

[tex]F = 12 N[/tex]

[tex]m_1 = 4 kg[/tex]

[tex]m_2 = 2 kg[/tex]

now we have

[tex]12 = (4 + 2) a[/tex]

so we have

[tex]a = 2 m/s^2[/tex]

now the force exerted by bigger block on smaller block is given as

[tex]F_n = ma[/tex]

[tex]F_n = (2 \times 2)[/tex]

[tex]F_n = 4 N[/tex]

now we know that two blocks will exert equal and opposite force on each other

so here the force exerted by 2 kg block on 4 kg block will be

[tex]F_n = -4 N[/tex]

The block of mass 2kg will exert a force of -4N on the block of mass 4kg

Third law of motion:

Two blocks of masses M = 4kg and m =2kg are given. The blocks are accelerated by a push of force F = 12 N applied to the 4kg block. So both the blocks move together.

Now, the equation of motion of the blocks is given by:

F = (M + m)a

12 = (4 + 2)a

so, the acceleration (a) is:

a = 2 m/s²

Thus, the force needed to move the block of mass 2 kg with this acceleration will be exerted by the block of mass 4kg and its magnitude will be:

f = ma

f = 2×2 N

f =4N

So the block of mass 4kg exerts a force of 4N on the block of mass 2kg.

Therefore, from Newton's third law of motion, the block of mass 2kg will exert an opposite and equal amount of force on the block of mass 4kg.

So, the block of mass 2kg exerts a force of -4N on the block of mass 4kg.

Learn more about laws of motion:

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