Determine the smallest force P that must be applied in order to cause the 150 -lb uniform crate

step 1 Okay, so this is the force diagram for the crates. And assume that the crates is in equilibrium,

Determine the smallest force P that must be applied in order...

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Key Concepts

Static Friction

Static friction is the resistive force that must be overcome to initiate the motion of an object at rest. It is described by the equation f? = ??N, where ?? is the coefficient of static friction and N is the normal force acting on the object.

Normal Force

The normal force is the perpendicular force exerted by a surface on an object in contact with it. It directly influences frictional forces because the maximum static friction is a function of the normal force, making it a key factor in determining whether an applied force is sufficient to start motion.

Equilibrium and Force Analysis

Analyzing the forces through a free-body diagram is essential to understand the balance of forces acting on an object. Establishing equilibrium and then determining the point at which an applied force exceeds static friction helps to calculate the minimum force required to initiate motion.

Transcript

00:01 Okay, so this is the force diagram for the crates.

00:06 And assume that the crates is in equilibrium, therefore the net force along the x -y direction should be equal 0.

00:13 So we have f minus p is equal 0, which means that f is equal to p.

00:16 F here is the friction on the crates, and p here is the force applied by the person.

00:22 And on y direction, we have n minus w is equal 0, which means that n is equal to w.

00:28 N is the normal force on the crates, w is the gravity of the crates.

00:31 And when the friction, in this case, can be equal to mu .sn, which is equal to mu.

00:36 M .s.

00:36 Here is the coefficient of the static friction.

00:40 So eventually you have p is equal to mu s .w.

00:43 And when you have mu .s is equal to 0 .5, w is equal to 150 pounds.

00:46 If we plug in battery equation with these values here, eventually you have the force p is equal to 75 pounds.

00:53 So now let's assume that the crate slides before, oh, sorry, here should be tipping, okay? so my assumption is that assume that the, crates, slides before tipping.

01:09 So now we can apply the moment at point a.

01:12 Consider counterclockwise moment is positive, clockwise moment is negative.

01:17 So we have p times 3 feet minus w times x is equal 0...

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