Circular accelaration with increasing velocity?

[Denken]

circular accelaration with increasing velocity?

Homework Statement

Object starts at rest at an angle of 0 degree's. the object is accelerated along a 45 degree arc with a radius of 2 meters to a speed of 7m/s at which point it is released. the object has a mass of .3 Kg. What is the equation for the force applied along the arc?

Homework Equations

circular accel. = V[2][/r] and other kinematics and derivatives and anti-derivatives

The Attempt at a Solution

way more work than i am going to put on here, but in the end i got a jerk function of 960.4/pi
... not fun

 

[americanforest]

To keep it in a circle you need a certain force. To accelerate it tangentially you need another. Superpose them to get the total force.

$$\vec{F}=-\frac{mv^{2}}{R}\hat{\rho}+F_{tan}\hat{\theta}$$

Then use basic kinematic equations with the information given to find the tangential force. Then it's just a matter of getting the magnitude, which we expect to be time dependent due to the centripetal contribution.

 

[Denken]

just a couple questions on that ... what does the {Rho} represent and why is it Ftan?

 

[americanforest]

The rho is the radial unit vector. Centrifugal forces push the mass out; in order for it to stay in a circle there needs to be an equal and opposite force pulling it in. This is what the force in the negative rho direction represents.

Mathematically,

$$\hat{\rho}=cos(\theta)\hat{x}+sin(\theta)\hat{y}$$

As for the other component of the force it is directed tangentially to the circle because it increases the tangential speed of the mass.

 

[rwisz]

I would say that the circular acceleration with increasing velocity is a result of the object's changing direction and speed as it moves along the arc. This can be explained by the equation for circular acceleration, which takes into account the object's velocity and the radius of the arc. The force applied along the arc can be calculated using Newton's second law, F=ma, where the mass and acceleration of the object are known. It is important to note that in this scenario, the force applied is not constant, as the object's velocity is increasing along the arc. This means that the force required to maintain the object's acceleration also increases.