Question

Two bodies A and B of masses 5 kg and 10 kg in contact with each other rest on a table against a rigid wall (Figure). The coefficient of friction between the bodies and the table is 0.15. A force of 200 N is applied horizontally to A. What are (a) the reaction of the partition (b) the action-reaction forces between A and B?What happens when the wall is removed? Does the answer to (b) change, when the bodies are in motion? Ignore the difference between μ_s and μ_k

Answer 1

(i) When the wall exists and blocks A and B are pushing the wall, there can’t be any motion i.e., blocks are at rest. Hence,

(a) reaction of the partition = – (force applied on A) = 200 N towards left.

(b) action reaction forces between A and B are 200 N each. A presses B towards right with an action force 200 N and B exerts a reaction force on A towards left having magnitude 200 N.

(ii) When the wall is removed, motion can take place such that net pushing force provides the acceleration to the block system. Hence, taking kinetic friction into account, we have

`200 - mu(m_1 + m_2)g = (m_1 + m_2)a`

`=> a   = (200 - mu(m_1+m_2)g)/((m_1+m_2)) = (200 - 0.15 xx (5 + 10)xx 10)/((5+10))`

`= (200-22.5)/15   = (177.5/15) = 11.8 ms^(2)`

∴if force excerted by A on B be `F_("BA")`, then considering equilibrium (or free body diagram) of only block A, we have

`200 - f_(k_1) = m_1a + F_"BA" or 200 - mum_1g = m_1a + F_"BA"`

`=> F_"BA" = 200 - mu m_1g - m_1a = 200 - (0.15 xx 5 xx 10) - (5xx11.8)`

=200 - 7.5 - 59

= 200 - 66.5 = 133.5 N `~~ 1.3 xx 10^2` n toward right

∴Force excerted on A by `B F_(AB) = - F_(BA) = 1.3 xx 10^2` N Toward left

Answer 2

(a) Mass of body A, m_A = 5 kg

Mass of body B, m_B = 10 kg

Applied force, F = 200 N

Coefficient of friction, μ_s = 0.15

The force of friction is given by the relation:

f_s = μ (m_A + m_B)g

= 0.15 (5 + 10) × 10

= 1.5 × 15 = 22.5 N leftward

Net force acting on the partition = 200 – 22.5 = 177.5 N rightward

As per Newton’s third law of motion, the reaction force of the partition will be in the direction opposite to the net applied force.

Hence, the reaction of the partition will be 177.5 N, in the leftward direction.

(b) Force of friction on mass A:

f_A = μm_Ag

= 0.15 × 5 × 10 = 7.5 N leftward

Net force exerted by mass A on mass B = 200 – 7.5 = 192.5 N rightward

As per Newton’s third law of motion, an equal amount of reaction force will be exerted by mass B on mass A, i.e., 192.5 N acting leftward.

When the wall is removed, the two bodies will move in the direction of the applied force.

Net force acting on the moving system = 177.5 N

The equation of motion for the system of acceleration a,can be written as:

Net force  =` (m_A + m_B)a`

`:. a = "Net force"/(m_A + m_B)`

`= (177.5)/(5+10) = (177.5)/15 = 11.83 "m/s"^2`

Net force causing mass A to move:

F_A = m_Aa

= 5 × 11.83 = 59.15 N

Net force exerted by mass A on mass B = 192.5 – 59.15 = 133.35 N

This force will act in the direction of motion. As per Newton’s third law of motion, an equal amount of force will be exerted by mass B on mass A, i.e., 133.3 N, acting opposite to the direction of motion