•A pendulum of mass of 600g is dropped from a height of 30cm.
•Calculate the GPE it had (g = 9.81)
•Tell me how much KE it will have at the bottom of its swing (assuming no air resistance)
•Assuming all the GPE is transferred to KE, what is the maximum velocity reached?
GPE = m * g * h = .6 * 9.81 * .3 J
KE = GPE
v = √(2 g h) m/s
To calculate the gravitational potential energy (GPE) of the pendulum at the starting position, you can use the formula:
GPE = mass × gravity × height
Given:
Mass of the pendulum (m) = 600g = 0.6kg
Height (h) = 30cm = 0.3m
Gravity (g) = 9.81 m/s²
Substituting these values into the formula:
GPE = 0.6kg × 9.81 m/s² × 0.3m
GPE = 1.7646 Joules
Therefore, the pendulum has 1.7646 Joules of gravitational potential energy at the starting position.
Now, let's calculate the kinetic energy (KE) at the bottom of the pendulum's swing.
The law of conservation of energy states that energy is conserved; therefore, the total mechanical energy at any point remains constant. In this case, assuming no air resistance, the total mechanical energy remains constant, meaning that the GPE will be converted entirely into KE.
So, at the lowest point of the swing, all the GPE will be converted into KE. Therefore, the KE is equal to the GPE at the starting position.
KE = GPE = 1.7646 Joules
Lastly, to find the maximum velocity reached, we can use the formula:
KE = 0.5 × mass × velocity²
Rearranging the formula to solve for velocity:
velocity = √(2 × KE) / mass
Substituting the values:
velocity = √(2 × 1.7646 Joules) / 0.6kg
velocity ≈ √(3.5292 Joules) / 0.6kg
velocity ≈ √5.882 Joule/kg
velocity ≈ 2.42 m/s
Therefore, the maximum velocity reached by the pendulum is approximately 2.42 m/s.