A 55.0kg box rests on a horizontal surface. The coefficient of static friction between the box and the surface is .300. What horizontal force must be applied to the box for it to start sliding along the surface? Please write out the solution. I am getting an answer of 165N but I don't think I wrote out the solution correctly.
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To find the horizontal force required to make the box start sliding along the surface, we need to compare the force of friction with the maximum frictional force that can be exerted before the box starts sliding.
The formula for the force of friction is given by:
Frictional force = Coefficient of friction * Normal force
In this case, the normal force is equal to the weight of the box, which is given by:
Normal force = mass * gravity
where the mass is 55.0 kg and the acceleration due to gravity is approximately 9.8 m/s^2.
Normal force = 55.0 kg * 9.8 m/s^2
Normal force = 539 N
Now, we can calculate the maximum frictional force that can be exerted by the box:
Maximum frictional force = Coefficient of static friction * Normal force
Given that the coefficient of static friction is 0.300, we have:
Maximum frictional force = 0.300 * 539 N
Maximum frictional force = 161.7 N
Therefore, in order to make the box start sliding, a horizontal force greater than the maximum frictional force must be applied. This means that the answer of 165 N that you obtained is correct.