Grade 12 Physics Help

[fletch to 99]

Hey everyone. So I'm currently doing a physics project and it involves making a mini launcher to launch a ball. With this launcher we have to be able to predict where the ball will land using calculations.

 

Here is the launcher I built (side view):

 

 

 

Basically the way it works is you put the ball at the top of the catapult looking device and push down, when you let go the spring pushes the arm up, launching the ball.

 

The only problem is I have no clue how to predict where it will land. My idea was to calculate the centripetal acceleration to find the velocity of the ball when it leaves the catapult and then from that turn it into a projectile motion problem which I know how to solve. The problem I ran into is centripital acceleration doesn't account for the angle of the launcher because the ball is not traveling in a complete circle.

 

Here is what I know:

 

Arm Length: 28cm

Arm travel distance: 28°

Spring Constant: 195 n/m

Approximate Travel distance using base setup: 203 cm (I found this by measuring where the ball landed in my test shots)

Launch Height using base setup: 62.23 cm

 

So my overall question is how can I find the launch velocity of the ball? Also my teacher stated that I must include elastic/kinetic/gravitational energy in my solution, that is why I calculated the spring constant.

 

Any help would greatly be appreciated.

 

[Artem]

This was one of my first physics problems in college. But that was a while ago so I wouldn't be able to help you... Man I'm glad I'm done with that crap lol. Good luck.

[fletch to 99]

This was one of my first physics problems in college. But that was a while ago so I wouldn't be able to help you... Man I'm glad I'm done with that crap lol. Good luck.

 

Thanks. I was like I'm set I'll just use centripetal acceleration... Until I realized that I have no way to calculate it for just the small angle that the launch arm travels. :

[Artem]

Thanks. I was like I'm set I'll just use centripetal acceleration... Until I realized that I have no way to calculate it for just the small angle that the launch arm travels. :

I had a professor that was very difficult to understand. Someone recommended for me to use THIS website for physics and math help. It really helped me a lot. Maybe you can find an answer to your problem there.

[alpenwasser]

I'm about to go to bed, so I can't solve this completely at the moment, however

you should be able to calculate the ball's initial velocity via the spring

constant, the ball's mass and the spring compression length.

You calculate how much energy is stored in the spring when it's compressed:

(I'm a bit rusty when it comes to mechanics, so you might want to re-check this

formula, but I think the basic principle is valid if I recall correctly.)

E_spring = 1/2 * k * delta_x^2

where

E_spring: energy stored in spring when compressed

k: spring constant

delta_x: length of compression

Disregarding friction, you can assume that all of this energy then gets

transferred to the ball, transforming the potential spring energy into

the ball's kinetic energy:

E_kin_ball = 1/2 * m_ball * v_initial_ball^2 = E_spring

where

E_kin_ball: Kinetic energy of ball at launch

m_ball: mass of ball (I'm assuming you can measure this)

v_initial_ball: initial velocity of ball at launch

Solve the above formula for v_initial_ball and you should have the launch

velocity of the ball. After that it's just a parabola flight dependent on

the launch angle, where the only forces acting on the ball are air resistance

and gravity. Depending on your problem, you may be allowed to ignore air

resistance, in which case the only force acting on the ball after launch

is gravity.

I definitely need to sleep now, but I think this should get you started.

EDIT:

I recommend googling around for parabolic trajectory of projectiles or

similar terms, this is a very common problem and you should be able to

find a solution like that.

[Glenwing]

Separate out the motion of the ball into X and Y components, instead of trying to fit a parabolic trajectory to it.  Once the ball launches it is travelling at a certain angle at a certain velocity; you can convert this into a certain velocity in the X direction plus a certain velocity in the Y direction, using the angle of release as they hypotenuse of a right triangle.  Start your calculations using the ball's initial position as your point of reference.  So the height of 62.23cm is treated as zero, and the horizontal position at the time of release is also zero.  The ground is now treated as being at a height of -62.23cm, that is its vertical position relative to the ball's initial position.  The X-velocity remains constant (in theory; in practice there is air resistance but it probably won't have much effect at this scale, depending on the ball material) and the Y-velocity has an acceleration of G (-9.8m/s).  Given the initial upwards Y-velocity at release that you calculated, and a Y-acceleration of -9.8m/s, calculate the time at which the ball will reach a height of -62.23cm (62.23cm below the initial position, where the ball was released), and then use that time to find the X-position at that time (since X-velocity remains constant, it will just be final time multiplied by the initial X velocity).  And, there you have the approximate horizontal distance from the catapult that the ball will be at, at the exact time the Y-position becomes ground-level.

 

Let me know if I should clarify any of that.

 

(As the other poster said, you should be able to figure out the ball's initial velocity from its mass and kinetic energy.  To find the kinetic energy you will need to see how much energy the spring releases when it springs, using the spring constant and the spring length.  The angle of the velocity of course is perpendicular to the catapult arm at the moment the ball is released).

[fletch to 99]

Separate out the motion of the ball into X and Y components, instead of trying to fit a parabolic trajectory to it.  Once the ball launches it is travelling at a certain angle at a certain velocity; you can convert this into a certain velocity in the X direction plus a certain velocity in the Y direction, using the angle of release as they hypotenuse of a right triangle.  Start your calculations using the ball's initial position as your point of reference.  So the height of 62.23cm is treated as zero, and the horizontal position at the time of release is also zero.  The ground is now treated as being at a height of -62.23cm, that is its vertical position relative to the ball's initial position.  The X-velocity remains constant (in theory; in practice there is air resistance but it probably won't have much effect at this scale, depending on the ball material) and the Y-velocity has an acceleration of G (-9.8m/s).  Given the initial upwards Y-velocity at release that you calculated, and a Y-acceleration of -9.8m/s, calculate the time at which the ball will reach a height of -62.23cm (62.23cm below the initial position, where the ball was released), and then use that time to find the X-position at that time (since X-velocity remains constant, it will just be final time multiplied by the initial X velocity).  And, there you have the approximate horizontal distance from the catapult that the ball will be at, at the exact time the Y-position becomes ground-level.

 

Let me know if I should clarify any of that.

 

(As the other poster said, you should be able to figure out the ball's initial velocity from its mass and kinetic energy.  To find the kinetic energy you will need to see how much energy the spring releases when it springs, using the spring constant and the spring length.  The angle of the velocity of course is perpendicular to the catapult arm at the moment the ball is released).

Thanks for the help. I never thought if converting elastic energy to kinetic energy. This will give me the initial velocity so I can solve for the trajectory. I've done the rest of this in previous labs.

[chicksoup]

maybe you can launch it a couple of times and figure out where it lands and somehow backtrace the steps of the calculation