a projectile with mass (m)=35grams is placed on a vertically positioned spring. the spring constant (k)=6500N/m. the projectile is launched straight up into the air by compressing the spring a distance (x)=8cm.How high does the projectile go?
To determine how high the projectile goes, we need to first calculate the potential energy stored in the spring and then convert it into gravitational potential energy.
1. Calculate the potential energy stored in the spring:
Potential Energy (PE) = (1/2) * k * x^2
PE = (1/2) * 6500 N/m * (0.08 m)^2
PE = 20.8 J (Joules)
2. Convert the potential energy of the spring into gravitational potential energy:
Gravitational Potential Energy (GPE) = m * g * h
We'll assume that the only significant force acting on the projectile is gravity (neglecting air resistance).
Where:
m = mass of the projectile = 0.035 kg (converted from grams)
g = acceleration due to gravity = 9.8 m/s^2 (approximate value on the Earth's surface)
h = height reached by the projectile (unknown)
Rearranging the equation, we can solve for h:
h = GPE / (m * g)
h = 20.8 J / (0.035 kg * 9.8 m/s^2)
h ≈ 60.31 m
Therefore, the projectile reaches a height of approximately 60.31 meters.