Question

Example 10.11 discusses the conversion of spring potential energy to kinetic energy. how much energy is initially stored in the spring?

A spring-loaded to gun is used to launch a 10 plastic ball. The spring, which has a spring constant of 10 N/m, is compressed by 10 cm as the ball is pushed into the barrel. When the trigger is pulled, the spring is released and shoot the ball back out horizontally.

Answer 1

The initial energy stored in the spring of a toy gun, with a spring constant of 10 N/m compressed by 10 cm, is calculated using the formula E = 1/2 k x². After converting the compression to meters, the energy is found to be 0.05 joules.

Step-by-step explanation:

Calculating Stored Energy in a Spring

The amount of energy stored in the spring of a toy gun can be found using the formula for the potential energy in the spring, which is E = 1/2 k x², where 'E' represents the elastic potential energy, 'k' is the spring constant, and 'x' is the displacement of the spring from its equilibrium position. In this case, the spring constant (k) is 10 N/m and the spring is compressed by 10 cm (which needs to be converted to meters, i.e., 0.1 m for correctness in units). Placing the given values into the equation yields:

E = 1/2 (10 N/m) (0.1 m)²

E = 1/2 (10) (0.01)

E = 0.05 J

Therefore, the initial energy stored in the spring is 0.05 joules.