Magnitude of a ball's Acceleration

AI Thread Summary
The discussion revolves around calculating the magnitude of a cue ball's acceleration after being struck by a cue stick. The user calculates the acceleration components and finds the overall magnitude to be approximately 145 m/s². However, there is confusion regarding the angle calculation and the use of significant figures, as the initial angle calculation may have incorrectly swapped the force components. The importance of significant figures is highlighted, suggesting that the final answer should reflect the two significant figures present in the initial data. The user seeks clarification on whether their calculations and understanding of significant figures are correct.
PhysicsHelp152
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Homework Statement



A 0.17-kg cue ball rests on the pool table. It's struck by a cue stick applying force F1→ = 13Ni^+21Nj^
Determine the magnitude of the ball's acceleration.

Homework Equations



ax = Fnet, x / m
ay = Fnet, y / m
a = Fnet / m

The Attempt at a Solution



Components of Acceleration:
ax = 13Ni^ / 0.17kg = 76.47m/s2

ay = 21Nj^ / 0.17kg = 123.53m/s2

Magnitude:
Fnet = √(13Ni^)2 * (21Nj^)2 = 24.7N

angle θ = tan-1 * (21N / 13N) = 58.24° above the + x-axis (fixed. see replies below)

Acceleration's Magnitude:
a = Fnet / m = 24.7N / 0.17kg = 145.29m/s2 or 145m/s2 rounded

I feel like this should be the answer, or that I'm very close to the answer. Am I missing a step? Did I do something wrong? Am I way off?
 
Last edited:
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Hi PhysicsHelp152, Welcome to Physics Forums.

Your work and results look fine except for the angle. Take another look at which component is which for the arctan function to find the angle w.r.t. the x-axis.
 
Is this the correct angle?
θ = tan-1 * (21N / 13N) = 58.24° (fixed. see replies below)

Also, the magnitude of the ball's acceleration is indeed 145m/s2?
I ask because apparently it isn't correct? I answer my questions online and I get 5 tries to get it right. I only have one try left and I already tried 145m/s2.
 
Last edited:
PhysicsHelp152 said:
Is this the correct angle?
θ = tan-1 * (21Ni^ / 13Nj^) = 58.24°
Yes, that looks better. But don't include the axis unit vectors in the formula: you're taking a ratio of component values, not vector quantities. Besides, the x-component is generally designated by the ##\hat{i}## unit vector, and the y-component by the ##\hat{j}## unit vector, and you seem to have swapped the components of the force vector by using "21Ni^" and "13Nj^".
Also, the magnitude of the ball's acceleration is indeed 145m/s2?
I ask because apparently it isn't correct? I answer my questions online and I get 5 tries to get it right. I only have one try left and I already tried 145m/s2.
Your calculation looks fine. You may be getting hit by significant figures. How many sig figs in the given information?
 
gneill said:
Your calculation looks fine. You may be getting hit by significant figures. How many sig figs in the given information?

There are 2 sig figs in the given information... I think. So my answer should be two sig figs?
But what would the answer be then?
 
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