A pendulum bob swinging at a velocity of 10 m/sec would rise how high from its lowest point of its swing
mv²/2=mgh
h= v²/2g
To calculate how high a pendulum bob would rise from its lowest point of swing, we need to consider the conservation of mechanical energy. The mechanical energy of the pendulum bob is the sum of its potential energy and kinetic energy:
E = PE + KE
At the lowest point of the swing, all of the pendulum bob's energy is in the form of kinetic energy, given by:
KE = (1/2) * m * v^2
Where:
- KE is the kinetic energy
- m is the mass of the pendulum bob
- v is the velocity of the pendulum bob
To determine how high the pendulum bob would rise, we need to find the point where the kinetic energy is completely converted into potential energy. At the highest point of the swing, all of the energy will be in the form of potential energy, given by:
PE = m * g * h
Where:
- PE is the potential energy
- m is the mass of the pendulum bob
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- h is the height from the lowest point of the swing
Since energy is conserved, we can equate the kinetic energy at the lowest point to the potential energy at the highest point:
(1/2) * m * v^2 = m * g * h
We can rearrange this equation to solve for h:
h = (v^2) / (2 * g)
Plugging in the values for v (10 m/s) and g (9.8 m/s^2), we can calculate h:
h = (10^2) / (2 * 9.8) = 51 m
Therefore, a pendulum bob swinging at a velocity of 10 m/s would rise approximately 51 meters from its lowest point of swing.