# Energy with springs on an angle

• desichick07
In summary, using the conservation of energy, we can find the launching speed of a 100g ball in a pinball machine with a spring constant of 1.2 N/cm and an inclined surface of 10 degrees. By converting the spring constant to 120 N/m and using the equation for potential energy stored in the spring, we can set that equal to the kinetic and gravitational potential energy at the moment the ball is launched. The angle is taken into account when finding the final height using the equation for potential energy. Solving for the velocity, we get ((mgh(f) - .5kx^2 )/(.5m))^.5, but since the distance is unknown, we cannot use this equation.
desichick07

## Homework Statement

The ball launcher in a pinball machine has a spring that has a constant of 1.2 N/cm. The surface on which the ball moves is inclined 10 degrees with respect to the horizontal. If the spring is initially compressed 5.0 cm, find the launching speed of a 100g ball when the plunger is released.

## Homework Equations

W = .5kx^2
mgh + .5kx^2 + .5mv^2 = mghf + .5kxf^2 + .5mvf^2

## The Attempt at a Solution

first i converted the spring constant
1.2 N/cm * 100cm/m = 120 N/m

next i found PE(spring)
.5kx^2 = .5(120N/m)(.05m)^2 = .15 J
then i used the mechanical energy eq...i canceled the unnecessary terms and got:
.5kx^2 + .5mv^2 = mgh(f)

and when i solve for V(initial) i get:
((mgh(f) - .5kx^2 )/(.5m))^.5

but then i don't know the distance which the ball travels so i can't use this equation
and also i know the 10 degrees has to factor in somewhere, but where? is it part of the potential energy of the string? or does it affect the initial velocity? or both?

first, W =! .5kx^2
Work = change in energy (not just energy)

I would use the conservation of energy to solve this problem
Energy stored in the spring = the kinetic energy of the ball right when its launched

The angle goes into the final height.

Your initial energy is the potential energy in the srping. Your final energy, right when the ball lleaves the spring, is kinetic and gravitational potentiall energy. You know everytheing but it's velocity. (draw a triangle to find h in mgh)

## 1. What is potential energy in a spring on an angle?

Potential energy in a spring on an angle refers to the energy stored in a spring when it is stretched or compressed at an angle to its equilibrium position. This energy is due to the elastic potential of the spring.

## 2. How is potential energy in a spring on an angle calculated?

The potential energy in a spring on an angle can be calculated using the formula PE = 1/2kx², where k is the spring constant and x is the displacement from the equilibrium position.

## 3. What is the relationship between the angle of the spring and potential energy?

The angle of the spring affects the potential energy by changing the distance the spring is stretched or compressed. The greater the angle, the greater the potential energy stored in the spring.

## 4. Can potential energy in a spring on an angle be converted into kinetic energy?

Yes, potential energy in a spring on an angle can be converted into kinetic energy when the spring is released. As the spring returns to its equilibrium position, the potential energy is converted into kinetic energy, causing the spring to oscillate.

## 5. How does the mass of an object attached to a spring on an angle affect potential energy?

The mass of an object attached to a spring on an angle does not directly affect the potential energy. However, it does affect the displacement of the spring, which in turn affects the potential energy. A heavier mass will result in a greater displacement and therefore, a greater potential energy stored in the spring.

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