A tilted spring
A projectile is on a spring of force constant k that is at an angle of 45 degrees and is compressed a distance of x, how high does the projectile go. I used conservation of energy and used the y component of x for the initial gravitational potential energy (which is negative). To get the final height, I set the initial gravitational energy plus the spring energy equal to the final gravitational energy when the kinetic energy becomes zero (the top of the curve). This apparently is giving me a larger number for height than the actual answer, what am I doing wrong?
Answer
Using energy is a good idea, but as with all physics problems there are many places you could go wrong. First, did you draw a picture of the situation? You will want to define your coordinate system and choose your height h = 0 where the gravitational potential energy is zero. The ground would be a good place to choose because you can draw it on your diagram!
Next, from what height is the projectile starting while it is loaded back into the spring? Does it start at h = 0, meaning it is stretched all the way to the ground? It looks like you may have plugged in the y-component of x, which is not the same situation.
Also, you said that you set the kinetic energy equal to zero at the top of the projectile's curve. However, if the projectile is fired at an angle it will always be moving horizontally even though it reaches a peak height, so there will always be some kinetic energy. Instead, you might try finding the velocity at which the projectile leaves the spring and treat it as a kinematic problem from that point onward.
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Using energy is a good idea, but as with all physics problems there are many places you could go wrong. First, did you draw a picture of the situation? You will want to define your coordinate system and choose your height h = 0 where the gravitational potential energy is zero. The ground would be a good place to choose because you can draw it on your diagram!
Next, from what height is the projectile starting while it is loaded back into the spring? Does it start at h = 0, meaning it is stretched all the way to the ground? It looks like you may have plugged in the y-component of x, which is not the same situation.
Also, you said that you set the kinetic energy equal to zero at the top of the projectile's curve. However, if the projectile is fired at an angle it will always be moving horizontally even though it reaches a peak height, so there will always be some kinetic energy. Instead, you might try finding the velocity at which the projectile leaves the spring and treat it as a kinematic problem from that point onward.