Center of Mass, Equilibriums help

[Syph]

Homework Statement

Hey, I'm just doing a physics assignment and I seem to be having some issues. Its all written answers and no calculations are needed. We are meant to learn this topic by ourselves (over the holidays) and that's why I'm having some trouble understanding some of the concepts. I need some help elaborating and explaining the topics. Like why does lowering the center of mass help a jumper ect.

Q1. Research and explain 3 types of equilibrium. (are mine correct?)
Q2. Explain why a truck standing still on an inclined road may or may not tip over. You need to discuss "restoring" and "non-restoring" torques.
Q3. Explain why High Jumpers can reach greater heights doing the "Fosbury Flop" rather than the more traditional "scissor" or "straddle" jumping styles.

Homework Equations

No equations. No calcs needed just explanations using diagrams and theorems.

The Attempt at a Solution

Q2.

http://img508.imageshack.us/img508/3073/stablecopyza7.jpg
(picture not displaying for some reason...)

As we can see from the above picture, if the center of mass lies outside the range of the base of support the system is unstable and in this case will topple.
If a system is applied torque and this causes the system to topple or reach a new equilibrium (unstable equilibrium) then this torque is classified a non-restoring torque. i.e. After applying a non-restoring torque the center of mass moves below the base of support. For example, if a person was to lean over to tie up their shoes they can do so without falling over as long as their center of mass stay above their base of support, the feet.
If a system is applied torque and this causes the system to return to its original equilibrium (stable equilibrium) this is known as a restoring torque.

Q3.

The Fosbury Flop is been the technique of choice for high jumpers since it was introduced into the sport in 1968. The athlete sprints diagonally towards the bar, jumps off his/her outside foot, then curves and leaps head-first, back downwards over the bar in a rolling motion keeping as much of the body as possible below the bar. When high jumpers perform this jump, they bend their body in such a way that it is possible for the athlete to clear the bar while his or her center of mass does not.
The main reason the flop is superior to previous high jump techniques (straddle, scissors, Eastern cutoff and Western roll) is that it allows the athlete to jump with a lower center of gravity, meaning more height can be cleared from the same energy input. It's possible for a jumper's center of gravity to pass beneath the bar using the Fosbury Flop technique.

Q1.

Mechanical Equilibrium (Static Equilibrium):
For a system to be in mechanical equilibrium the force and reaction are balanced and the system remains unchanged over time. Or in other words the net forces and moments must equal 0 (i.e. no rotational or translational acceleration).

Stable Equilibrium:
The system is said to be in stable equilibrium when after disturbed the system displays tendencies to return to its original equilibrium.
e.g. A square tool (used for checking right angles in many jobs) tapped slightly returns to its original stable position after wobbling (returns to equilibrium after disturbance). The center of mass after the disturbance was higher than it was originally allowing the square to return to its original equilibrium.
Unstable Equilibrium:
A system is in unstable equilibrium when after a disturbance, the system return to a new but different equilibrium.
e.g. The same square tool used in the stable equilibrium is positioned differently and then tapped which causes it to topple and stop laying flat on the table. A new equilibrium has been reached. The center of mass in this example has moved downwards after the disturbance which causes the square to fall reaching a new equilibrium.

 

[member38644]

Q1. Your explanations of mechanical equilibrium, stable equilibrium, and unstable equilibrium are all correct. Another type of equilibrium that could be mentioned is neutral equilibrium, where the system remains in equilibrium even after being disturbed.

Q2. In the case of a truck standing still on an inclined road, there are two main factors that determine whether it will tip over or not: the angle of the incline and the location of the truck's center of mass. If the incline is not too steep and the center of mass is within the base of support (the area between the wheels), the truck will not tip over. This is because the restoring torque (caused by gravity pulling down on the center of mass) is greater than the non-restoring torque (caused by gravity pulling down on the front of the truck). However, if the incline is too steep or the center of mass is outside of the base of support, the non-restoring torque will be greater and the truck will tip over.

Q3. As mentioned in the question, the Fosbury Flop allows the high jumper to have a lower center of mass than the traditional jumping styles. This lower center of mass allows for a greater distance between the center of mass and the bar, which means that the athlete can clear the bar while their center of mass is still below it. In the traditional styles, the center of mass would have to pass over the bar, making it more difficult to clear with the same amount of energy input. This is why the Fosbury Flop allows for greater heights to be reached.

 

[m2003]

Hello, it is great that you are taking the initiative to learn the topic on your own during the holidays. I understand that it can be challenging to grasp some concepts without a teacher present to explain them. I will do my best to help you understand the topics of center of mass and equilibrium.

Center of mass is the point at which the mass of an object is evenly distributed. It is often referred to as the "balance point" of an object. The position of the center of mass is important in determining the stability of an object. In the case of a jumper, lowering the center of mass can help by increasing stability. This is because the lower the center of mass, the more difficult it is for the object (in this case, the jumper) to topple over. This is due to the fact that a lower center of mass means that the weight is distributed more evenly, making it more difficult to tip over.

Q1. There are three types of equilibrium: stable, unstable, and neutral equilibrium. You have correctly defined stable and unstable equilibrium. Neutral equilibrium is when the system remains in equilibrium but does not return to its original position after a disturbance. An example of this is a ball resting at the bottom of a bowl. When the ball is pushed, it will stay at the new position, but will not return to the bottom of the bowl.

Q2. In the case of a truck standing still on an inclined road, the restoring torque would be the weight of the truck acting downwards towards the ground. This torque would be balanced by the normal force from the ground acting upwards. If the truck is at a steep angle, the weight may not be enough to balance the normal force, causing the truck to tip over. This is an example of a non-restoring torque, as the truck would not return to its original position after the disturbance.

Q3. The Fosbury Flop allows for a lower center of mass compared to the traditional jumping styles. This is because the athlete is able to curve and roll over the bar, keeping their body below the bar. This in turn allows for a larger base of support, making it more difficult for the athlete to topple over. The traditional jumping styles, such as the scissor or straddle, require the athlete to have a higher center of mass and a smaller base of support, making it easier to tip over.

I hope this helps you understand the topics of center of mass and equilibrium better. If you have