Two crates, of mass 78 kg and 103 kg, are in contact and at rest on a horizontal surface (Fig. 4-47). A 729 N?

Two crates, of mass 78 kg and 103 kg, are in contact and at rest on a horizontal surface (Fig. 4-47). A 729 N force is exerted on the 78 kg crate.

if the coefficient of friction is .15 what is the force that each crate exerts on the other?

Two crates, of mass 78 kg and 103 kg, are in contact and at rest on a horizontal surface (Fig. 4-47). A 729 N?
OK let T be the force acting between the masses. By Newton's law, this force has an equal and opposite reaction on each of them.

For each of them, the normal reaction is equal to its weight, and the friction equal to μ*mg



Forces on the 78 kg mass:

729 - T - 78*0.15*9.81 = 78*a ...(1)

where a = common acceleration of both masses



Forces on the 103 kg mass:

T - 103*0.15*9.81 = 103*a ...(2)



Now you need to solve (1) and (2) si multaneously to get a and T.

a = 2.556 m/s^2

T = 414.8 N
Reply:Instead of thinking the two masses as separate, we can consider them as a single mass of

[78 +103] = 181kg.

Now a force of 729 N is acting on the single mass and a frictional force of

0.15 x 181 x 9.8 = 266.7N is opposing the motion.

The net force is 729 - 266.7 = 462.3 N



Acceleration = F/m = 462.3/181= 2.554 m/s^2

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Now consider the two masses as two separate masses,

but each moving with the same acceleration of

2.554 m/s^2



For the mass 103 kg to move with an acceleration of 2.554 m/s^2 a force = ma must act on it.

ma =103 x 2.554 = 263.062 N.



This is the force exerted by the 78 kg on this mass of 103 kg.

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Since this is action force, the reaction force is 263.062 N and is exerted by the 103 kg mass on the 78 kg mass.

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We can verify this as follows.

For the mass 78 kg to move with an acceleration of 2.554 m/s^2 a force = ma must act on it.

ma =78 x 2.554 = 199.212 N.



This is the net force acting on the mass of 78 kg alone acting in the direction of net applied force

Of 462.3 N. Therefore the other mass has exerted a force of 462.3 - 199. 212N = 263.088 N.

Hence verified.

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