How Do You Calculate the Speed of a Ball in Rotational Motion?

AI Thread Summary
To calculate the speed of a ball in rotational motion, the tension force must be broken into vertical and horizontal components, with the vertical component balancing the weight of the ball. The equation tan(30°) = v² / (rg) can be used, where r is determined by the length of the cord and the angle. To find the maximum speed with a tension limit of 9.8 N, the correct approach involves recalculating the angle, as the tension and weight create a different angle than initially assumed. The maximum speed is ultimately determined to be 4.7 m/s when the tension is at its limit. Understanding the relationship between tension, weight, and angle is crucial for accurate calculations in this scenario.
crispy_nine
Messages
6
Reaction score
0
Hey, I've puzzled my puzzler sore on this question for my physics assignment:

A 0.50-kg ball that is tied to the end of a 1.5-m light cord is revolved in a horizontal plane with the cord making a 30° angle with the vertical. (a) Determine the ball’s speed. (b) If the cord can withstand a maximum tension of 9.8 N, what is the highest speed at which the ball can move?

If anyone could help me out that would be awesome.
Cheers,
Chris
 
Physics news on Phys.org
Let Ft = force of tension Fg = weight Fnet = net centripetal force

The key is to break the tension force into vertical and horizontal components. The vertical component will be equal to the weight. The horizontal component will be equal to the net centripetal force. If you write an equation for each of these, and then divide the second one by the first one you get:
tan 30 = v^2 / (rg) where r = 1.5 m sin 30

Does that help?
 
Thanks a lot, I understand how to find the velocity, but I'm still doing something wrong to get the max possible V if max T can be 9.8N. Ty = mg= 4.9N. What I'm doing to find max V is finding max Tx...so sqrrt(9.8^2 - 4.9^2) = 8.49N = (m X v^2)/ 1.5msin30. This is apparently wrong...the correct answer is 4.7m/s.
 
When the tension is 9.8N and the weight is 4.9N, the angle between srting and the vertical is not 30 degree but 60 degree. Try it again.
 
Last edited:
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
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}...
Back
Top