Tangential and centripetal force

[robax25]

Homework Statement

The canister of a juicer has 333 grams of pulp distributed over its inside wall at an average radius of 8.00cm. It starts from rest and reaches its maximum angular speed of 3600.0 rpm in 4.00 seconds. For the pulp, determine ( f ) the tangential and centripetal force on it at t = 2.00s and t = 4.00s. my question why tangential force is constant and centripetal force is varying?

Homework Equations

tangential force F=ma =m ∝ r
centripetal force= mv²/r
3. The Attempt at a Solution

Ft = Mat ; ( Ft )1 = ( 0.333 kg )( 7.54 m/s2 ) = 2.51 N ; ( Ft )2 = 2.51 N (Constant tangential force)

Fc = Mac ; ( Fc )1 = ( 0.333 kg )( 2850 m/s2) = 949 N

( Fc )2 = ( 0.333 kg )( 11400 m/s2) = 3800 N ( Variable centripetal force)

 

[Delta2]

I suppose along with the problem is given a diagram of angular speed with respect to time ? The tangential force can be (depends on that diagram) constant because the tangential velocity is $v=\omega r$ and if from the diagram we can infer that $\omega=at$ (in other words the diagram is a straight line) for constant $a$ then the tangential force will be $F_t=m\frac{dv}{dt}=mar$ which is constant in time since a and r are constant.

 

[robax25]

In this case acceleration is constant but if uniform circular motion than tangential force would be zero? Am I right?

 

[Delta2]

Yes, in uniform circular motion the tangential acceleration and force are zero, it wouldn't be uniform otherwise.

 

[robax25]

when tangential force is varying in Circular motion?

 

[Delta2]

When the angular speed varies with time in any other way except linear.

 

[Chestermiller]

when tangential force is varying in Circular motion?

What is the equation for the tangential acceleration of a particle at constant radial distance from the center of rotation if the angular velocity is changing?

 

[robax25]

tangential acceteration at= α r

 

[robax25]

When the angular speed varies with time in any other way except linear.

this is main reason that tangential acceleration is constant when linear acceleration...and when there is no linear acceleration than tangential acceleration will vary. Am I right?

 

[Chestermiller]

this is main reason that tangential acceleration is constant when linear acceleration...and when there is no linear acceleration than tangential acceleration will vary. Am I right?

Huh?

 

[Delta2]

tangential acceteration at= α r

That is true only in the case where angular acceleration is constant (or equivalently when angular velocity varies linearly with respect to time).

I think the general equation that answers Chet's question is

$a_{tan}=\frac{d\omega(t)}{dt}r$.

 

[haruspex]

That is true only in the case where angular acceleration is constant (or equivalently when angular velocity varies linearly with respect to time).

I think the general equation that answers Chet's question is

$a_{tan}=\frac{d\omega(t)}{dt}r$.

I suggest that robax25 meant a_t=αr, which is the same as your equation.
at=αr, as in acceleration x time, would never be correct.

 

[haruspex]

when tangential force is varying in Circular motion?

I do not understand your question. Please state it completely.

 

[haruspex]

why tangential force is constant and centripetal force is varying?

First, it is a bit inaccurate to speak of tangential force here. Force is a vector and has a specific direction. There are lots of infinitesimal tangential forces acting in different directions around the circumference. Better to speak of torque.

The answer comes from inspection of the equations. If the torque is constant but nonzero, what is happening to the angular velocity? How does angular velocity, at a given radius, relate to centripetal acceleration?
Or maybe you understand this from the equations, but are looking for a more intuitive explanation?

 

[robax25]

my last question..when centripetal force is constant? In my problem, centripetal force varies in certain interval but when it is constant?

 

[haruspex]

my last question..when centripetal force is constant? In my problem, centripetal force varies in certain interval but when it is constant?

That is still not a complete question. What is it that you are asking about the case when it is constant?

 

[robax25]

when centripetal force is constant? We get centripetal force when there is a circular motion. I think my question is clear.If there is a uniform circular motion or a non-uniform circular motion, which case centripetal force is constant? In my problem, there is constant acceleration and that's why, centripetal force varies in every seconds. my question when centripetal force remains constant in respect of time?

 

[haruspex]

when centripetal force remains constant in respect of time?

Ah, you mean "when is centripetal force constant?", not "when centripetal force is constant". The first is a question, but the second is a statement of circumstance.
The centripetal acceleration is the component of acceleration that is orthogonal to the velocity. In uniform circular motion that has constant magnitude, and in non-uniform circular motion it does not, but there are also other motions in which it may have constant magnitude.