Explaining Work & Accel. of Particle Moving in Circular Path

AI Thread Summary
A particle moving in a circular path at constant speed experiences a resultant force acting at right angles to its path, as work is defined as the product of force and displacement in the direction of the force. If the force were aligned with the path, it would result in infinite work being done, causing the particle's speed to increase. The direction of acceleration must be towards the center of the circle to maintain circular motion; without this centripetal force, the particle would move in a straight line. The discussion emphasizes that the centripetal force is always perpendicular to the velocity of the particle, ensuring constant speed. Understanding these principles is crucial for analyzing motion in circular paths.
garytse86
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I have got a prolem here: a particle is moving along a circular path at constant speed, use the definition of the term work to explain why the resultant force acting on the particle must be acting at right angles to its path.

Also why must the direction of the acceleration be towards the centre of the circle?

Thank you very much.

Gary
 
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Also why must the direction of the acceleration be towards the centre of the circle?
If it wasn't, the object would move in a straight line.

Regards
 
Does the speed or kinetic energy of the object change?

How much work is the "centripetal" force doing on the object? (Centripetal is in quotes because, for the purposes of the excercise, you cannot assume that the force is towards the center of the circle.)

What does that tell you about the force acting on the particle.

dlgoff:
There is a differece between having a component that is perpendicular to the velocity, and being entirely perpendicular to the velocity. For example, in parabolic motion where the initial velocity is perpendicular to the force, the particle is obviously not traveling in a straight line, but the force is only initially perpendicular to the velocity.
 
Originally posted by garytse86
I have got a prolem here: a particle is moving along a circular path at constant speed, use the definition of the term work to explain why the resultant force acting on the particle must be acting at right angles to its path.

W = Fd.

If the force was inline with the path, it would mean infinite work is being done, and the rotation speed would increase.


Also why must the direction of the acceleration be towards the centre of the circle?

Draw a picture of a guy holding a rope connected to something like a rock. If the guy swings the rock around at a constant speed, where is the force coming from? The only force I see is the rope connected to the rock; which is perpendicular to the motion of the rock.
 
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thanks a lot.
Gary
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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