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Two crates of mass 75 kg and 110 kg are in contact and at rest on a horizontal surface. A 730 N force is exerted on the 75 kg crate, and the coefficient of kinetic friction between the surface and crates is 0.15. Find the force that each crate exerts on the other.

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Final answer:

The larger 110 kg crate exerts a backward force of 272.25 N on the 75 kg crate when a 730 N force is applied to it due to the acceleration caused by the net force after overcoming kinetic friction.

Step-by-step explanation:

To find the force that the 75 kg and 110 kg crates exert on each other when a 730 N force is exerted on the 75 kg crate, we must first calculate the frictional force affecting them.

The total mass of the system is 75 kg + 110 kg = 185 kg.

The normal force for the system is therefore the combined weight of both crates, i.e., (185 kg)(9.8 m/s2) = 1813 N.

Using the coefficient of kinetic friction, μk = 0.15, the total kinetic frictional force opposing the motion is μk N = 0.15 * 1813 N = 271.95 N.

Since the crates are in contact and move together as a single system, the 730 N force must overcome the frictional force for both crates.

Therefore, the net force accelerating the system is 730 N - 271.95 N = 458.05 N.

To find the acceleration, we use Newton's second law: Fnet = ma, meaning a = Fnet / m = 458.05 N / 185 kg = 2.475 m/s2.

The force that each crate exerts on the other is due to this acceleration.

The larger crate (110 kg) will exert a backward (to the 75 kg crate) force equal to its mass times the acceleration, which is (110 kg)(2.475 m/s2) = 272.25 N.

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