Question

A spring powered dart gun is unstretched and has a spring constant 100 N/m. The spring is compressed by 8 cm and a 5 gram projectile is placed in the gun. The maximum height of the projectile(from its compressed position) when it is shot straight up from the gun is?

Answer 1

To find the maximum height of the projectile, we can use the principle of conservation of mechanical energy. The maximum height is 6.53 meters.

Step-by-step explanation:

To find the maximum height of the projectile, we can use the principle of conservation of mechanical energy. The spring potential energy is converted into gravitational potential energy when the projectile reaches its maximum height. Here's how to calculate it:

1. Convert the spring compression distance from centimeters to meters: 8 cm = 0.08 m
2. Calculate the potential energy of the spring when it is compressed: potential energy = 0.5 * spring constant * (compression distance)^2 = 0.5 * 100 N/m * (0.08 m)^2 = 0.32 J
3. Set the spring potential energy equal to the gravitational potential energy at maximum height: potential energy = mass * gravity * height => 0.32 J = 0.005 kg * 9.8 m/s^2 * (height)
4. Solve the equation for the height: height = 0.32 J / (0.005 kg * 9.8 m/s^2) = 6.53 m

The maximum height of the projectile when shot straight up from the gun is 6.53 meters.