How can I calculate the acceleration of a baseball thrown by a pitcher?

[vxr]

Homework Statement

A pitcher throws a baseball of mass m = 0.15 kg accelerating it from rest to velocity v = 60km/h. Estimate the force exerted by the pitcher on the ball. If needed, make a reasonable assumption for the distance over which the pitcher accelerates the ball.

Relevant Equations

F = ma

Hello. I have just started studying physics. Can someone explain to me how can I type in formulas here using Tex for nicer formatting?

I suppose the force is F = ma.
Question is: what is a?

The starting throw angle is not mentioned, I suppose this task has to be related to gravity. All I know is the mass of the ball and velocity 60 km/h which is I suppose final velocity the ball has just before it hits the ground.

I do know calculus and I heard that acceleration is derivative of velocity. Just not sure how to apply derivation in here as I kind of never solved any physics task before.

Thanks for tips.

 

[Chestermiller]

Is this just a problem you invented yourself, or is it out of some textbook?

 

[vxr]

It's a task the teacher provided us with at our first physics class. I double checked and I've rewritten it correctly.

 

[gneill]

You might want to think about what other kinematic formulas might be helpful here. Remember that you first need to estimate the distance through which the throw acts, so a kinematic formula involving distance and the other things you are given should prove useful.

 

[Chestermiller]

It's a task the teacher provided us with at our first physics class. I double checked and I've rewritten it correctly.

Are you allowed to specify/estimate the amount of time the force is applied?

 

[PeroK]

It's a task the teacher provided us with at our first physics class. I double checked and I've rewritten it correctly.

You could ask your teacher a question:

Does he/she think a constant force would be applied in this case?

You could give him/her a hint: is there a relationship between power, force and velocity?

 

[Chestermiller]

https://www.physicsforums.com/help/latexhelp/

 

[vxr]

Thank you all, your answers gave me some context on how should I approach physics problems and what kind of questions I should be asking myself.

I will attempt easier problems.

 

[haruspex]

Your teacher must want you to assume the force is constant. That allows you to use the SUVAT equations to find the acceleration from the initial and final velocities and the distance over which the force is applied.

Alternatively, your teacher is under the mistaken impression that you can find the average of a varying force by equating energy as force x distance with gained KE. That does not give average force, which is defined as change in momentum divided by time.

 

[vxr]

I have a small question about horizontal acceleration.

Let's say there's a tall man who throws a ball in parallel to the ground. Because of vertical acceleration (gravitation), the ball eventually falls. Also, the initial velocity is smaller than the final velocity, because of the acceleration I assume.

So the ball accelerates.

My questions:

0. Is the initial velocity = 0 or does it have some value? To me it only makes sense that initial velocity is non-zero positive value. I feel like if the initial velocity was = 0, then the ball would only be able to fall straight down and not move an inch into right --> direction. It simply does not make sense to me that the initial velocity would be 0. I assume the man applies the force onto the ball the moment he releases it from his hand, and at that very moment it gains some initial velocity that is different than 0...

1. Is there any initial horizontal acceleration? What happens with that horizontal acceleration throughout the ball's flight? (is it decreasing? increasing? constant? or there is no horizontal acceleration at all?)

2. Moreover I am curious about this: let's assume vacuum and no gravity at all. The same tall man throws a ball. In my opinion there should not be any acceleration. The velocity should be constant and equal to initial speed. Is this correct?

So if second question is 'true' and there is no acceleration at all, then the answer to the first question should be: no horizontal acceleration at all (or: putting aside gravity, there is no other acceleration).

Thus in my opinion in both cases there is some initial velocity, but no acceleration. (first case there's only gravity acceleration, and no other 'magic' acceleration)

Not sure if these questions make any sense but I'd greatly appreciate some help here.

 

[DrClaude]

Let's say there's a tall man who throws a ball in parallel to the ground. Because of vertical acceleration (gravitation), the ball eventually falls. Also, the initial speed is smaller than the final speed, because of the acceleration I assume.

I'm assuming here that you are discussing what happens once the ball leaves the pitchers hand.

1. Is there any initial horizontal acceleration? What happens with that horizontal acceleration throughout the ball's flight? (is it decreasing? increasing? constant? or there is no horizontal acceleration at all?)

The have an acceleration, you have to a force acting on the ball. What forces can you see opposing the motion of the ball?

2. Moreover I am curious about this: let's assume vacuum and no gravity at all. The same tall man throws a ball. In my opinion there should not be any acceleration. The velocity should be constant and equal to initial speed. Is this correct?

In this case, both the speed and the velocity will be constant. (What is the difference between speed and velocity?)

So if second question is 'true' and there is no acceleration at all, then the answer to the first question should be: no horizontal acceleration at all (or: putting aside gravity, there is no other acceleration).

For a real baseball thrown on Earth? Think about the conditions you set in point 2 above.

 

[vxr]

Still quite struggling with that one. Did I solve it correctly?

Assume that $s = 2.5m$

$v_{f}^2 = v_{0}^2 + 2as$

$a = \frac{v_{f}^2 - v_{0}^2}{2s}$

$a = \frac{16.6^2 - 0^2}{2*2.5}$

$a =~ 55 \frac{m}{s^2}$

This is correct, right? Or..

Anyway, if that's correct then I suppose $F_{net} = ma = 0.15 * 55 = 8.25 N$

Answer: $8.25 N$

Is $s = 2.5m$ a reasonable assumption?

 

[Chestermiller]

That 2.5 meters seems way high to me. When a pitcher delivers the ball, his hand is in contact with the ball 1 meter, max. And what kind of wimpy pitcher throws the ball at 16.6 m/s? A major league pitcher delivers a fastball at more than 40 m/s.

 

[haruspex]

That 2.5 meters seems way high to me. When a pitcher delivers the ball, his hand is in contact with the ball 1 meter, max. And what kind of wimpy pitcher throws the ball at 16.6 m/s? A major league pitcher delivers a fastball at more than 40 m/s.

Bizarrely, all the instances of this question I can find online take the acceleration distance to be 3m or more. One of them didn't specify a distance but took the time as 0.43s; that would make more sense as the time to reach the batter!
A youtube video of Drew Storen clearly shows it is much closer to 1m.

But my bigger gripe with this problem, as mentioned, is the assumption of constant acceleration over that distance. In the early parts of the delivery, most of the acceleration is in the pitcher's body, then the arms. It is akin to cracking a whip, with a progressive transfer of momentum to the lighter components.
The acceleration of the ball is principally in the last 10% of the time. See section 3 at https://res.mdpi.com/proceedings/pr...edings-02-00206-v2.pdf?filename=&attachment=1.