Physics questions - center of gravity, etc. Pls check my answers.?

Question

1. What's the use of knowing the center of gravity?
2. Is the center of gravity of a meterstick always located at the 50cm mark?
3. What do drivers mean when they say the car needs wheel balancing?
4. A traffic signal light is suspended by the cables. Under what condition will the tension be equal to the weight of the signal light?
5. Is it possible for the center of gravity to lie outside the body?
6. Does the center of gravity always coincide with the geometrical center of objects?

My answers: 1. for balance? 2. Yes (because it's a regular shaped object?) 3. wheel balancing - allows tires to spin without causing vibrations. 4. translational equilibrium (first) 5. Yes. 6. No (for irregularly shaped objects?)

Are my answers correct? Any more additional info to be added is appreciated. Thanks!

Answer 1

1) The center of gravity is the point at which gravity appears to act if the object was a point source. Balance is one reason to know the center of gravity/mass of an object. It is also very useful in aeronautics as the center of gravity must fall in certain parameters for a craft to be stable. In some cases for military fighter aircraft, the center is off balance to give added maneuverability.

2) Yes, as you said. It's a regular shaped object, also defined as uniform object. This means the density does not change over the stick's length.

3) it means that there is an even distribution of weight on both sides of the car. As you mentioned an uneven distribution will cause vibrations and uneven wear on your car's tires. It can also impact your car's safety.

4) If you are referring to one cable suspending the signal, then it's when the cable is directly above the center of mass of the signal. If they are more than once cable, then they too will be directly above the center of mass. The sum of the individual tensions will the the weight of the signal light.

5) Yes, In the case of large planetary bodies; the moon-Earth system for example, the center of mass is different from the center of gravity. On the small scale, what most of us encounter in our day to day lives they are the same.

6) No, if the object is not of uniform density it will not coincide with the geometrical center. In other words, the way the mass is distributed will affect how that center falls.

Answer 2

I disagree with you on #4. If the tension = weight, the light and cables are hanging straight down from its support. Normally it's hanging from a more or less horizontal cable. Tension is much higher than weight in that arrangement.

In #6, your comment in ( ) doesn't quite hit it. More if the density of material is irregular.

Answer 3

The apple is inside you and still possesses its potential energy. When you return to the ground, both you and the apple will lose your potential energy.