What is the magnitude of the average force that her neck exerts on her head during the landing?

What is the magnitude of the average force that her neck...

Key Concepts

Impulse-Momentum Theorem

This theorem states that the impulse delivered to an object (the product of the average force and the time interval over which it acts) is equal to the change in the object’s momentum. In problems involving impacts or collisions, this concept helps in understanding how forces over brief time intervals can result in significant changes in motion.

Newton’s Second Law

Newton’s Second Law relates the net force acting on an object to its mass and the acceleration it undergoes (F = ma). This principle is fundamental for analyzing the forces experienced during dynamic events, such as the deceleration of the head upon impact, by linking the force to changes in velocity over time.

Average Force

The average force is a simplified representation of a possibly varying force over a time interval, calculated as the total impulse divided by the duration of the impact. It is especially useful in collision problems where the exact force profile might be complex but an overall effect is needed to analyze the motion and energy changes.

Momentum

Momentum is defined as the product of an object's mass and its velocity, serving as a measure of the quantity of motion. In impact situations, evaluating the change in momentum helps determine the forces involved by connecting mass, velocity changes, and time intervals through the impulse-momentum relationship.

Transcript

00:01 Okay, so this is one of those rare multiple choice problems, but let's just go ahead and start recording information.

00:08 So we are told that the mass of one's head is some fraction of that person's body.

00:16 So let's just go ahead and calculate that right off the bat.

00:20 So the mass of your head is 9 .4 % the mass of your body.

00:25 So if we take that equal to 65 kilograms, then we get the mass of our head.

00:30 Head is 6 .11 kilograms.

00:34 The dancer begins at a velocity of 4 meters per second.

00:41 And then because of an interaction between the neck and the head, we come to rest afterward.

00:48 Over a time interval of 200 milliseconds or 0 .20 seconds.

00:57 Great.

00:58 And then before we move on, we should also draw a body diagram.

01:03 So we're modeling the body, kind of like a little block place it with your head being on top of the rest of your body.

01:12 And in this interaction where we're coming to rest, let's drop free body diagram off the side here.

01:19 Of course, there is always the omnipresent force of gravity, but again, we're slowing down.

01:26 So there's a normal force that is greater than the force due to gravity.

01:32 Actually, i will modify this in order to say that we're starting off at negative 4 .0 meters per second because we just fell, we just jumped off of something, and then we're coming to a halt now...

Please give Ace some feedback