A 57-kg lead ball is dropped from the leaning tower of Pisa. The tower is 56 m high.
(b) What is the speed of the ball after it has traveled 2.5 m downward?
change in potential energy = (1/2) m v^2 = m g (2.5)
v^2 = 2 (9.8)(2.5)
v = 7 m/s
mass does not matter
To determine the speed of the ball after it has traveled 2.5 m downward, we need to use the principles of physics.
We can start by calculating the potential energy of the ball when it's dropped from the leaning tower of Pisa. The potential energy (PE) can be calculated using the formula:
PE = m * g * h
Where:
m = mass of the ball (57 kg)
g = acceleration due to gravity (9.8 m/s^2)
h = height of the tower (56 m)
PE = 57 kg * 9.8 m/s^2 * 56 m
PE = 31,752 Joules
The potential energy is converted into kinetic energy as the ball falls, assuming no other forces are acting on it. The kinetic energy (KE) is given by the equation:
KE = 1/2 * m * v^2
Where:
m = mass of the ball (57 kg)
v = velocity of the ball
Since the ball is not at the ground yet, we can use the conservation of mechanical energy to find the final velocity at a specific height. The sum of the potential energy and the kinetic energy will remain constant throughout the motion.
Initial mechanical energy (E_initial) = PE
Final mechanical energy (E_final) = PE + KE
At a height of 2.5 m, we can calculate the final velocity (v_final) using the equation:
E_final = PE + KE = E_initial
And solve it for v_final:
KE = E_final - PE
1/2 * m * v_final^2 = E_final - PE
Substituting the known values, we have:
1/2 * 57 kg * v_final^2 = 31,752 Joules - 57 kg * 9.8 m/s^2 * 2.5 m
Now, we can solve for v_final:
v_final = √[(31,752 J - 57 kg * 9.8 m/s^2 * 2.5 m) * 2 / 57 kg]
By evaluating this expression, we can find the velocity of the ball after it has traveled 2.5 m downward from the leaning tower of Pisa.