A 0.05 kg toy is made up of a spring of constant 466 N/m. When you place the toy on the floor, the spring 5 cm and release it, the toy jumps upwards. What is in Joules the spring potential energy stored in the toy when sitting on the floor with a cocked spring? Use 10 m/s2 for g
To calculate the spring potential energy stored in the toy, we need to use the formula for spring potential energy:
Potential energy = (1/2) * k * x^2
Where:
- Potential energy is the energy stored in the spring (in Joules)
- k is the spring constant (in N/m)
- x is the displacement of the spring from its equilibrium position (in meters)
In this case, we are given:
- The mass of the toy: 0.05 kg
- The spring constant: 466 N/m
- The displacement of the spring: 5 cm = 0.05 m
First, we need to calculate the force exerted by the toy's weight on the spring. The force can be calculated using Newton's second law of motion:
Force = mass * acceleration
The acceleration is equal to the acceleration due to gravity (g), which is given as 10 m/s^2. Thus, the force exerted by the toy is:
Force = 0.05 kg * 10 m/s^2 = 0.5 N
Now, we can calculate the potential energy using the formula mentioned earlier:
Potential energy = (1/2) * k * x^2
Potential energy = (1/2) * 466 N/m * (0.05 m)^2
Potential energy = (1/2) * 466 N/m * 0.0025 m^2
Potential energy = 0.29125 J (rounded to 5 decimal places)
Therefore, the spring potential energy stored in the toy when sitting on the floor with a cocked spring is approximately 0.29125 Joules.