Question

A spring-loaded dart gun has a spring with a spring constant of 3091 N/m that is compressed a total distance of 0.06 m before being released. The mass of each dart is 0.017 kg. How high in meters does the dart go above the gun if the dart is fired straight up?

Answer 1

The dart will go above the gun a height of approximately 0.1007 meters.

Step-by-step explanation:

To find the height that the dart will go above the gun, we can use the principles of elastic potential energy and conservation of mechanical energy. In this case, the initial potential energy stored in the compressed spring is converted into gravitational potential energy as the dart is propelled upwards. The equation to calculate this height is:

PE_spring = PE_gravity

(1/2)kx^2 = mgh

Where:

• k = spring constant (3091 N/m)
• x = distance the spring is compressed (0.06 m)
• m = mass of the dart (0.017 kg)
• g = acceleration due to gravity (9.8 m/s²)

Plugging in the given values, we can calculate the height as:

h = (1/2)kx^2 / mg

h = (1/2)(3091 N/m)(0.06 m)^2 / (0.017 kg)(9.8 m/s²)

h ≈ 0.1007 m.