Energy difference between stop and 90 degree deflection.

[lightningbob]

Ok to make this easy let's start with a 10 lb Bowling ball (let's even say 10 inch diameter) moving at 10 mph. What is the difference in the forward force (energy) required to stop the ball verses the energy applied the move the ball through a 90 degree curve with a 20 inch diameter arc. In short what force lbs would be measured by both assuming everything is the same except for the 90 degree bend in one.

 

[Lsos]

The energy required to stop it is the same as that required to start it. However, to turn it 90 degrees doesn't require energy. Satellites are constantly turning without using energy.

Both scenarios require force, however. You cannot use energy and force interchangeably.

 

[DragonPetter]

The energy required to stop it is the same as that required to start it. However, to turn it 90 degrees doesn't require energy. Satellites are constantly turning without using energy.

Both scenarios require force, however. You cannot use energy and force interchangeably.

I think it does require energy to turn anything. How does a satellite turn without using energy? If it has an angular momentum, then that angular momentum came from an initial energy source.

You are right that force and energy are not interchangeable, but any time a force is exerted, whether it be over a distance or it be through the torque on an object, energy has been exerted.Anyway, the energy in the second scenario, a force must be applied perpendicular to the direction of the moving ball to force it to curve off at a tangent. The amount of foce is simply the component of force perpendicular to the direction that the ball is moving times the distance in that component direction that the ball was moved during the force transfer. I don't have time to work out the numbers for you though, sorry.

 

[ecneicS]

You are right that force and energy are not interchangeable, but any time a force is exerted, whether it be over a distance or it be through the torque on an object, energy has been exerted.

Nope. There is something called gravity (pronounced /ˈgravitē/) that is exerting a force on me. According to E = F*d, the energy caused by the force of gravity on me is zero because I have not moved. You are right that an exerted energy quantity can be associated with the force, but it is zero.

 

[bp_psy]

I think it does require energy to turn anything. How does a satellite turn without using energy? If it has an angular momentum, then that angular momentum came from an initial energy source.

If a constant force would spontaneously start acting perpendicular to the trajectory of a particle moving at a constant speed ,the particle would start moving in a circle. There would be no actual gain in angular momentum since the speed of the object and the distance from the central point would be constant. Of course such a system does not exist but for some bowling moving around a bend it's probably a good rough approximation

 

[DragonPetter]

If a constant force would spontaneously start acting perpendicular to the trajectory of a particle moving at a constant speed ,the particle would start moving in a circle. There would be no actual gain in angular momentum since the speed of the object and the distance from the central point would be constant. Of course such a system does not exist but for some bowling moving around a bend it's probably a good rough approximation

Nope? So you're telling me that a force exerted over a distance or through a torque does not always mean energy has been exerted? Because that's what I said : "any time a force is exerted, whether it be over a distance or it be through the torque on an object, energy has been exerted"

 

[DragonPetter]

If a constant force would spontaneously start acting perpendicular to the trajectory of a particle moving at a constant speed ,the particle would start moving in a circle. There would be no actual gain in angular momentum since the speed of the object and the distance from the central point would be constant. Of course such a system does not exist but for some bowling moving around a bend it's probably a good rough approximation

First, constant speed or constant force are irrelevant, they don't have to be constant. If a force is applied to the object that causes its position to change, whether that be angular or not, energy has been used to make this change.

Secondly, the actual change to start moving the ball in a circle as you describe means that the angular momentum has changed, since it was not moving in a circle originally.

How can you argue that changing the direction of the bowling ball in his second case doesn't require energy?

 

[bp_psy]

First, constant speed or constant force are irrelevant, they don't have to be constant. If a force is applied to the object that causes its position to change, whether that be angular or not, energy has been used to make this change.

As I said that system is not realistic because you can't have a force starting to act spontaneously perpendicular to the trajectory of some object.Force does not produce motion ,it produces change in velocity.This does not necessarily mean change in energy since change in velocity =/= change in speed.

Secondly, the actual change to start moving the ball in a circle as you describe means that the angular momentum has changed, since it was not moving in a circle originally.

No it has exactly as much angular momentum as before since L=rXp(=mvr for circular motion) . Note an object doesn't have to move in circle to actually have angular momentum.

How can you argue that changing the direction of the bowling ball in his second case doesn't require energy?

I don't I just say that is not due to some change in angular momentum with respect to the center of the circular path.

 

[Lsos]

I think it does require energy to turn anything. How does a satellite turn without using energy? If it has an angular momentum, then that angular momentum came from an initial energy source.

A satellite is constantly turning. The Earth has been turning for billions of years and it continues to do so without an input of energy.

Sure it had to get some initial energy to be in orbit in the first place. Where that energy came from is beyond the scope of this discussion. The bowling ball also got some initial energy from the bowler. That's also beyond the scope. OP's question begins with the bowling ball already in motion.

You are right that force and energy are not interchangeable, but any time a force is exerted, whether it be over a distance or it be through the torque on an object, energy has been exerted.

"Any time force is exerted", "over a distance", and "through the torque" are completely different scenarios. The only scenario in which energy is required is when force acts "over a distance". In the other scenarios energy is not required, and indeed we encounter countless situations everyday when it is not expended.

Anyway, the energy in the second scenario, a force must be applied perpendicular to the direction of the moving ball to force it to curve off at a tangent. The amount of foce is simply the component of force perpendicular to the direction that the ball is moving times the distance in that component direction that the ball was moved during the force transfer. I don't have time to work out the numbers for you though, sorry.

If the force acting on the ball is always perpendicular to its motion, then the force will turn the ball while acting on 0 distance. This means you don't need energy. Such is the case with a satellite, a flywheel, or (possibly) a bowling ball. Theoretically the bowling ball should require no energy to change it's direction. The only losses will be due to friction.

 

[lightningbob]

Ok let me start over a ten inch diameter, ten pound ball is accelerated to ten mph in ten inches. It is easy to calculate the force pounds on the back wall of the tube the ball is in (not the force exerted on the ball). As the ball travels down the tube it goes thru a ninety degree twenty inch diameter curve. How do we calculate the force on the tube only in the exact opposite direction from the first force measurement. So if two scales were were placed in opposition from each other what would the first read ( when the ball is accelerated) and the second when the balls course is changed. Don't take into account gravity or drag.

 

[Lsos]

V^2 = 2ad solve for a to find acceleration of the ball to 10mph.
a = v^2/r solve for a to find acceleration around the curve.
f = ma use this to find force of either scenario.