Calculating energy Conservation

Question

A compressed spring in a toy is used to launch a 0.05 Kg ball. If the ball leaves the toy with an initial horizontal speed of 5.00 meters per second, and the spring constant is 50 N/m, what is the compressed amount? ( Energy Conservation EPE to KE).

Answer 1

Step 1: Write down the relevant formulas 1. Elastic Potential Energy (EPE): EPE = (1/2) * k * x^2 where k = 50 N/m and x = compressed distance (unknown). 2. Kinetic Energy (KE): KE = (1/2) * m * v^2 where m = 0.05 kg and v = 5.00 m/s.

Step 2: Set EPE equal to KE Since all the potential energy in the spring is converted into kinetic energy: (1/2) * k * x^2 = (1/2) * m * v^2

Step 3: Simplify the equation Cancel out the (1/2) terms on both sides: k * x^2 = m * v^2 Now, solve for x (the compressed amount).

Step 4: Calculate x Substitute the known values: x^2 = (m * v^2) / k x^2 = (0.05 * 25) / 50 x^2 = 1.25 / 50 x^2 = 0.025 x = sqrt(0.025) = 0.158 m

Final Answer: The compressed amount of the spring is: x = 0.158 m (or 15.8 cm)