# Spring Questions about ball launcher

• dustpal
In summary, the ball launcher in a pinball machine has a spring that has a force constant of 1.20 N/cm. The surface on which the ball moves is inclined 10.0° with respect to the horizontal. If the spring is initially compressed 4.50 cm, find the launching speed of a 80 g ball when the plunger is released. Friction and the mass of the plunger are negligible.
dustpal
I need help ASAP because the teacher assigned it today and its due tomorrow...

## Homework Statement

The ball launcher in a pinball machine has a spring that has a force constant of 1.20 N/cm. The surface on which the ball moves is inclined 10.0° with respect to the horizontal. If the spring is initially compressed 4.50 cm, find the launching speed of a 80 g ball when the plunger is released. Friction and the mass of the plunger are negligible.

## Homework Equations

Fs = -kx
Ws = change in KE
KE = 0.5mv^2
w = mg

## The Attempt at a Solution

w(x)=mg*sin(10) >>>>>> w(x)=0.136 N
Fs = -(1.2)(-4.50) >>>>> Fs = 5.4 N
F(netx)= Fs - w(x) >>>> 5.4 - 0.136 >>>>> F(netx) = 5.264 N
Ws = Fd >>>> Ws = 5.264*0.0450 >>>>> Ws = 0.23688 J
Ws = 0.5mv^2 >>>>> 0.23688 = 0.5(0.08)V^2 >>>>> v = 2.43 m/s (which is about twice as much as it should be)

## Homework Statement

A light spring with spring constant k1 is hung from an elevated support. From its lower end a second light spring is hung which has spring constant k2. An object of mass m is hung at rest from the lower end of the second spring.
(a) Find the total extension distance of the pair of springs. (Use k1 for k1, k2 for k2, and m and g as appropriate in your equation.) (b) Find the effective spring constant of the pair of springs as a system. We describe these springs as in series. (Use k1 for k1 and k2 for k2 as appropriate in your equation.)

## Homework Equations

Fs = -kx
w = mg
Ws =Fd = change in KE
KE = 0.5mv^2

## The Attempt at a Solution

Honestly, we didn't really cover springs all too well in our physics class so i have no clue where to even begin, just a hint would help me so much. The one example we did was on a horizontal plane so that's why i think I'm having difficulties doing vertical and inclined springs.

dustpal said:
I need help ASAP because the teacher assigned it today and its due tomorrow...

## Homework Statement

The ball launcher in a pinball machine has a spring that has a force constant of 1.20 N/cm. The surface on which the ball moves is inclined 10.0° with respect to the horizontal. If the spring is initially compressed 4.50 cm, find the launching speed of a 80 g ball when the plunger is released. Friction and the mass of the plunger are negligible.

## Homework Equations

Fs = -kx
Ws = change in KE
KE = 0.5mv^2
w = mg

## The Attempt at a Solution

w(x)=mg*sin(10) >>>>>> w(x)=0.136 N
Fs = -(1.2)(-4.50) >>>>> Fs = 5.4 N
F(netx)= Fs - w(x) >>>> 5.4 - 0.136 >>>>> F(netx) = 5.264 N
Ws = Fd >>>> Ws = 5.264*0.0450 >>>>> Ws = 0.23688 J
Ws = 0.5mv^2 >>>>> 0.23688 = 0.5(0.08)V^2 >>>>> v = 2.43 m/s (which is about twice as much as it should be)

## Homework Statement

A light spring with spring constant k1 is hung from an elevated support. From its lower end a second light spring is hung which has spring constant k2. An object of mass m is hung at rest from the lower end of the second spring.
(a) Find the total extension distance of the pair of springs. (Use k1 for k1, k2 for k2, and m and g as appropriate in your equation.) (b) Find the effective spring constant of the pair of springs as a system. We describe these springs as in series. (Use k1 for k1 and k2 for k2 as appropriate in your equation.)

## Homework Equations

Fs = -kx
w = mg
Ws =Fd = change in KE
KE = 0.5mv^2

## The Attempt at a Solution

Honestly, we didn't really cover springs all too well in our physics class so i have no clue where to even begin, just a hint would help me so much. The one example we did was on a horizontal plane so that's why i think I'm having difficulties doing vertical and inclined springs.
In the first problem, it is best to use energy methods, but if you do it your way, you must first note that the 5.4N spring force is the maximum force exerted by the spring. Its average force is 1/2 that amount. Secondly, your formula for Ws =Fd = 1/2 mv^2 is an incorrect application of the work energy theorem, not only because you must use the average force, but also because you neglected the work done by gravity. So rather than get bogged down with average forces and work, use the conservation of energy theorem
$$PE_{spring}_{initial} + PE_{ball}_{initial} + KE_{ball}_{initial} = PE_{spring}_{final} + PE_{ball}_{final} + KE_{ball}_{final}$$ . Do you know how to calculate or find each of these terms?

Last edited:
well...we aren't allowed to use energy conservation yet because we haven't learned it. If u could help correct what i have, that would be the best way. But i don't understand what u mean by avaerage force and stuff. isn't everything at an instant?

dustpal said:
well...we aren't allowed to use energy conservation yet because we haven't learned it. If u could help correct what i have, that would be the best way. But i don't understand what u mean by avaerage force and stuff. isn't everything at an instant?
This problem is difficult using Newton only. You say you didn't learn energy conservation , but you do have some sort of formula relating to work and energy, so that means you have studied work energy methods but not the conservation of energy principle? Do you know the formula for PE of a spring??And regarding 'average' forces in a spring, when you use F = kx, the force is 0 when x is 0, then builds up to a maximum force when x is at its final displacement. The average force is kx/2. Thus, the work done by the spring is F_avg(x) = kx/2(x) = 1/2kx^2.

dustpal said:

## Homework Statement

The ball launcher in a pinball machine has a spring that has a force constant of 1.20 N/cm. The surface on which the ball moves is inclined 10.0° with respect to the horizontal. If the spring is initially compressed 4.50 cm, find the launching speed of a 80 g ball when the plunger is released. Friction and the mass of the plunger are negligible.

## Homework Equations

Fs = -kx
Ws This should be W_net= change in KE
KE = 0.5mv^2
w = mg

## The Attempt at a Solution

w(x)=mg*sin(10) >>>>>> w(x)=0.136 N
Fs = -(1.2)(-4.50) >>>>> Fs = 5.4 NThus, F_avg = 5.4/2 =2.7N
F(netx)= F_avg - w(x) >>>> 2.7 - 0.136 >>>>> F(netx) = 2.564 N
Ws should be W_net= F_net(d) >>>> W_net = 2.564*0.0450 >>>>> W_net = 0.11538 J
W_net = 0.5mv^2 >>>>> 0.11538 = 0.5(0.08)V^2 >>>>> v = 1.7 m/s (which is about what it should be)

[Honestly, we didn't really cover springs all too well in our physics class so i have no clue where to even begin, just a hint would help me so much. The one example we did was on a horizontal plane so that's why i think I'm having difficulties doing vertical and inclined springs.
Maybe too late, but check out my comments in red. I don't like doing the problem this way, but it works.

woah, that solved all the problems...like even my other ones similar to this one, you are a lifesaver...i think, idk, we'll see the results later. although...my other has me finding the x(max)...which I'm finding to be almost impossible again

Last edited:

## What is a ball launcher?

A ball launcher is a device used to launch or throw a ball. It is designed to provide enough force for the ball to travel a certain distance.

## How does a ball launcher work?

Most ball launchers use a spring mechanism to launch the ball. The spring is compressed by pulling back the launching arm or lever, and when released, the spring expands and propels the ball forward.

## What types of balls can be used with a ball launcher?

There are various types of ball launchers, each designed for specific types of balls. Some common types of balls used with ball launchers include tennis balls, baseballs, and golf balls.

## Can a ball launcher be used for different sports?

Yes, some ball launchers are designed for specific sports, while others are more versatile and can be used for different sports. For example, a tennis ball launcher can also be used for pickleball or baseball.

## Is a ball launcher safe to use?

While ball launchers can be a fun and convenient way to play, it is important to always follow safety precautions. Be sure to read and follow the instructions carefully, and use appropriate protective gear when necessary.

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