The mass m=1.00 kg is set up as a pendulum of length 0.6m . Initially in the position of h=0.2 m above the lowest point, and the pendulum is given initial speed of 1.00 m/s. What is the largest mass M that could be temporarily lifted in such setup?
To find the largest mass M that could be temporarily lifted in the given setup, we need to consider the conservation of mechanical energy.
The total mechanical energy of the system is given by the sum of potential energy (PE) and kinetic energy (KE):
E = PE + KE
The potential energy of the mass m is given by:
PE = mgh
Where:
m = mass (1.00 kg)
g = acceleration due to gravity (9.8 m/s²)
h = height above the lowest point (0.2 m)
The kinetic energy of the mass m is given by:
KE = 0.5mv²
Where:
v = velocity (1.00 m/s)
Since the pendulum is given an initial speed and not an initial angle, we can assume that the speed it is released with remains constant throughout its motion.
Initially, when the mass m is at its highest point, all of its mechanical energy is potential energy:
E_initial = mgh
When the mass m reaches its lowest point, all of its mechanical energy is kinetic energy:
E_final = 0.5mv²
Since mechanical energy is conserved, E_initial = E_final:
mgh = 0.5mv²
We can solve this equation for the unknown mass M by substituting the values:
Mgh = 0.5mv²
Dividing both sides of the equation by gh:
M = 0.5v² / g
Substituting the given values:
M = 0.5(1.00 m/s)² / (9.8 m/s²)
M = 0.25 kg / 9.8 kg/s²
M = 0.025 kg
Therefore, the largest mass M that could be temporarily lifted in the given setup is 0.025 kg.