Average acceleration of a ball

In summary, a 45.0 g Super Ball traveling at 30.0 m/s bounces off a brick wall and rebounds at 21m/s. The ball is in contact with the wall for 3.0ms. Using the equation average acceleration=final velocity-initial velocity/time interval, the average acceleration of the ball during this time interval can be calculated to be -17000m/s^2. The negative sign indicates that the acceleration is in the opposite direction of the initial velocity. The magnitude of the acceleration is 17000m/s^2, meaning that the ball experienced a significant change in velocity during its time in contact with the wall.
  • #1
chocolatelover
239
0

Homework Statement


A 45.0 g Super Ball traveling at 30.0 m/s bounces off a brick wall and rebounds at 21m/s. A high-speed camera records this event. If the ball is in contact with the wall for 3.0ms, what is the magnitude of the average acceleration of the ball during this time interval? (It should be positive)


Homework Equations


1ms=10^-3s
average acceleration=final velocity-initial velocity/time interval


The Attempt at a Solution



21-30/3-0=-3ms

1ms(10^-3s/-3ms)=-.00033

but this can't be right because it's negative, right?

Thank you very much
 
Last edited:
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  • #2
chocolatelover said:

Homework Statement


A 45.0 g Super Ball traveling at 30.0 m/s bounces off a brick wall and rebounds at 21m/s. A high-speed camera records this event. If the ball is in contact with the wall for 3.0ms, what is the magnitude of the average acceleration of the ball during this time interval?


Homework Equations


1ms=10^-3s
average acceleration=final velocity-initial velocity/time interval


The Attempt at a Solution



21-30/3-0=-3ms

1ms(10^-3s/-3ms)=-.00033

but this can't be right because it's negative, right?

Thank you very much
The negative is OK, but your magnitude is incorrect. You must watch your plus and minus signs in your designations of the initial and final velocities...they are in different directions. Also, if you end up with a negative for the acceleration, you should interpret its meaning.
 
  • #3
I am not sure if you have gotten to impulse, but if you have, then you can solve with those equations. Recall that linear momentum J equals the change in impulse - J=mv2-mv1

Also remember that J=Favg*T
You'll have solved for J, and you already know that T=3 ms, so you should be able to find your average force during this period of time. Your average force should equal mass times your average acceleration.
F=ma
a=Favg/m

That's how I would solve it. Let me know if that helps.
 
  • #4
Thank you very much
 
  • #5
Does this look correct?

I know that the average acceleration=velocity/time

So couldn't I do the following?

Average acceleration=-21-30/3-0
= -17

In order to find the magnitude, I would need to put this in scientific notation, right?

-1.7 X 10^1

The magnitude would be 1, right?

Thank you very much
 
  • #6
You have got to be consistent with your units. The average acceleration is the change in velocity over the change in time. Velocity is given in meters per second; you should therefore first convert 3 milliseconds to seconds, before doing the division. What will be the units of the acceleration?

Magnitude means 'how much', it does not refer to the scientific notation exponent; it just means "how much is the acceleration?" You don't necessarily have to convert to scientific notation, although it sometimes makes the result clearer by avoiding a lot of zeros.
 
  • #7
Thank you very much

Does this look right?

-21-30/.003-0= -17000

1000ms=1s
3ms=.003

But it says that it should be positive

Thank you
 
  • #8
chocolatelover said:
Thank you very much

Does this look right?

-21-30/.003-0= -17000

1000ms=1s
3ms=.003

But it says that it should be positive

Thank you
math is good, but what are the units of the acceleration? The magnitude of the acceleration is 17,000 (____) (fill in the blank with the correct units; if the velocity is in m/s and the time is in seconds, what are the units of the acceleration?).
 
  • #9
Thank you very much

Regards
 
  • #10
chocolatelover said:
Thank you very much

Regards
You are welcome. Oh, by the way, you got a negative value because you assumed the initial velocity of the ball was positive to the right, and its final velocity was negative to the left, thus it's change in velocity was Vf-Vi= -21-30= -51m/s , where the minus sign means that the velocity change, and hence the acceleration, is to the left. The magnitude of the acceleration is just the absolute value ,or a positive number, of 17000m/s^2. The negative indicates the direction.
 

What is average acceleration of a ball?

The average acceleration of a ball is a measure of how quickly the velocity of a ball changes over a given period of time. It is typically expressed in meters per second squared (m/s^2).

How is average acceleration of a ball calculated?

The average acceleration of a ball can be calculated by dividing the change in velocity (final velocity minus initial velocity) by the time interval over which the change occurs.

What factors can affect the average acceleration of a ball?

The average acceleration of a ball can be affected by various factors such as the initial velocity, mass of the ball, and the presence of any external forces such as friction or air resistance.

Can the average acceleration of a ball be negative?

Yes, the average acceleration of a ball can be negative if the ball is slowing down. This means that the velocity is decreasing over time.

How is the average acceleration of a ball different from instantaneous acceleration?

The average acceleration of a ball is the overall change in velocity over a given time interval, while instantaneous acceleration is the acceleration at a specific moment in time. Average acceleration considers the entire motion, while instantaneous acceleration only considers a single point in time.

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