85 lb force is applied to the 200lb crate, which is stationary before the force is applied. Determine the force exerted by the horizontal surface on the crate

Assuming the crate is on a horizontal surface, so gravity is dedicated to the normal reaction N = 200 lb. force, and the 85 lb.force applied is used to overcome the static friction offered by the horizontal surface.

Therefore the (resistive) force exerted by the horizontal surface is equal to the applied force of 85 lb. force.
We have assumed that after the force is applied, the crate either remains stationary or moves with a uniform velocity.

well

To determine the force exerted by the horizontal surface on the crate, we need to apply Newton's second law of motion.

Newton's second law states that the force exerted on an object is equal to the mass of the object multiplied by its acceleration. The equation is:

Force = Mass x Acceleration

In this case, the mass of the crate is given as 200 lb. However, we need to convert this mass from pounds to slugs since the equation is in the Imperial system. The conversion factor is 1 lb = 0.03108 slugs. Therefore, the mass of the crate in slugs is:

Mass = 200 lb x 0.03108 slugs/lb = 6.216 slugs (rounded to three decimal places)

Now, the force applied to the crate is given as 85 lb. We also need to convert this force to slugs. Using the same conversion factor, the force applied is:

Force = 85 lb x 0.03108 slugs/lb = 2.641 slugs (rounded to three decimal places)

Since the crate is stationary before the force is applied, its initial velocity (v₀) is zero. Consequently, the equation we'll be using is:

Force exerted = Mass x Acceleration

Rearranging the equation:

Acceleration = Force exerted / Mass

Now we can calculate the acceleration:

Acceleration = 2.641 slugs / 6.216 slugs = 0.424 ft/s² (rounded to three decimal places)

Therefore, the force exerted by the horizontal surface on the crate is equal to the mass of the crate (200 lb) multiplied by its acceleration:

Force exerted = Mass x Acceleration
Force exerted = 6.216 slugs x 0.424 ft/s² = 2.638 lb (rounded to three decimal places)

Hence, the force exerted by the horizontal surface on the crate is approximately 2.638 pounds.