Here is a diagram of a person at rest holding a push-up...

Here is a diagram of a person at rest holding a push-up position. Assume that the person weigh 180 lb, which acts at the point shown. Assume the following lengths a=15 in, b=44 in, and c=18 in. Your goal is to determine the normal force exerted by the floor on each of hands and on each foot. General approach/hints: Draw the free body diagram for the forces. Write an equation to describe sum of forces. Write an equation to describe moment due to the forces (For example, where hands of come to contact with the ground). Use system of equations (2 equations + 2 unknowns) to solve for the force on each hand and on each foot.

Transcript

00:01 In this video, we're going to be looking at static equilibrium.

00:05 Okay, and that's the state in which an object is at rest.

00:08 So stationary, not moving.

00:13 And what we have for our system is a person holding a stationary plank position.

00:19 Okay, like so.

00:21 And what i want to find is the normal force that the ground exerts on this person's feet and hands.

00:29 Okay.

00:29 In order for this person to remain stationary, so to remain in static equilibrium.

00:36 So let's look at some numbers.

00:38 Okay, we have the distance from this person's hands to his center of mass.

00:43 A is 15 inches.

00:45 The distance from the center of mass to this person's feet is 44 inches.

00:49 His center of mass is 18 inches above the ground, and this person weighs 180 pounds.

00:56 And we'll be using these values once we get our expressions for.

00:59 The force of the hands and the feet.

01:02 Okay, so let's start looking at that.

01:04 For a system in static equilibrium, we know the sum of all forces acting on the object must be equal to zero, and the sum of all torques about some rotation point must equal to zero.

01:15 Now let's set up our coordinate system.

01:18 I'm calling the upward direction positive, downward direction is negative.

01:22 I'm going to set my rotation axis at this person's center of mass or gravity there.

01:29 All right, so now we'll only have two forces that contribute a torque.

01:33 We'll have the force of the hands and the force of the feet.

01:36 Let's define our directionality there for our rotation.

01:39 I'm going to call forces that tend to cause a counterclockwise rotation about the rotation axis.

01:46 I call that the negative direction.

01:49 Okay, so clockwise will be positive.

01:52 Right, so now we're ready to set up our force and torque balances.

01:56 So they both equal to zero.

01:58 Both of those sums are zero.

01:59 Start with force.

02:01 Okay, we have the force on the hands from the floor and that's positive...

Question

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