Tangential Acceleration vs. Tangential component of force

AI Thread Summary
The discussion revolves around calculating the tangential component of force for a ball moving in a circle while accelerating. The tangential acceleration is determined to be 10.47 m/s², calculated using the formula at = αr. The participant initially calculates the tangential force as 1.3 N, but receives partial credit, indicating a possible error in vector notation. The key point raised is that components of vectors should not include unit vectors, suggesting the correct answer should be presented without the t-hat notation. Clarification on vector representation is essential for accurate problem-solving in physics.
jumbogala
Messages
414
Reaction score
4

Homework Statement


A ball moves counterclockwise in a circle and is speeding up. The radius of the circle is 5 m.

Its angular acceleration is α, (2.09 rad/s2)\hat{k}

The ball's mass is 0.125 kg.

What is the tangential component of the force on the particle?

Homework Equations


The Attempt at a Solution


So the tangential acceleration is at = αr = 10.47 m/s2\hat{t}

(Define \hat{t} to be tangent to the circle. At the top of the circle, it points to the left. At the bottom, it points to the right and so on).

Then the tangential component of the FORCE on this particle should be (10.47 m/s2)\hat{t} * 0.125 kg = (1.3 N)\hat{t}

But I got it wrong, and I have no clue why. Can anyone help me out? I got half the marks so it may just be a small error somewhere =\
 
Last edited:
Physics news on Phys.org
The calculation looks OK. Components of vectors do not have unit vectors attached to them. Try without the t-hat.
 
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}...
View full post »

Similar threads

Tangential acceleration and centripetal acceleration
Replies
5
Views
2K
Tangential and centripetal force
Replies
17
Views
2K
Tangential Acceleration Problem, UCM
Replies
2
Views
1K
Why is the tangential force not same?
Replies
10
Views
2K
Centripetal and Tangential Acceleration
Replies
1
Views
3K
Normal and tangential components of acceleration
Replies
21
Views
4K
Angular acceleration, tangential acceleration
Replies
6
Views
2K
Angle between radius and acceleration
Replies
4
Views
1K
Calculating tangential acceleration of rotating object
Replies
2
Views
3K
What is the net acceleration of the coin on a rotating disk?
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top