A small ball with a mass of 30.0 g is loaded into a spring gun, compressing the spring by 13.0 cm. When the trigger is pressed, the ball emerges horizontally from the barrel at a height of 2.30 m above the floor. It then strikes the floor, after traveling a horizontal distance of 2.40 m. Use g = 9.80 m/s2. Assuming all the energy stored in the spring is transferred to the ball, determine the spring constant of the spring.

I tried to use conservation of energy. 1/2 kx^2 = mg(h2-h1). But i don't get the answer.

Are you from BU? haha.

1/2kx^2=1/2mv^2, the v here is vx final, solve for k

To solve this problem using conservation of energy, you need to consider the potential energy stored in the spring when it is compressed and the potential energy gained by the ball when it is lifted to a certain height.

Let's go step by step through the problem:

1. Write down the given information:
- Mass of the ball (m) = 30.0 g = 0.030 kg
- Compression of the spring (x) = 13.0 cm = 0.13 m
- Height above the floor (h2) = 2.30 m
- Horizontal distance traveled (d) = 2.40 m
- Gravitational acceleration (g) = 9.80 m/s^2

2. Calculate the potential energy stored in the spring (Us):
The potential energy stored in a spring is given by the formula: Us = (1/2)kx^2, where k is the spring constant.

Us = (1/2)kx^2

3. Calculate the potential energy gained by the ball (Uh):
The potential energy gained by the ball when raised to a certain height is given by the formula: Uh = mgh, where m is the mass of the ball, g is the gravitational acceleration, and h is the height.

Uh = mgh2

4. Set up an equation using conservation of energy:
According to the principle of conservation of energy, the potential energy stored in the spring should be equal to the potential energy gained by the ball:

Us = Uh

(1/2)kx^2 = mgh2

5. Solve for the spring constant (k):
Rearrange the equation and substitute the given values into it:

k = (2mgh2) / x^2

k = (2 * 0.030 kg * 9.80 m/s^2 * 2.30 m) / (0.13 m)^2

By calculating this expression, you should get the value of the spring constant (k).