A sophomore chemistry student holds a 500mL Erlenmeyer flask full of concentrated nitric acid high above his head at a height of 1.75 meters and declares, "I'm the King of Chemistry!" At that moment another student, startled by the sudden ignition of her Bunsen burner, jumps back and bumps into the King, who drops the flask. How long until the flask breaks all over his royal sneakers?
hf=ho+1/2 g t^2
0=1.75-4.9 t^2 solve for t.
To determine how long it takes for the flask to break all over the student's sneakers, we need to consider the gravitational potential energy and the impact force on the flask.
The potential energy of an object at a certain height is given by the formula:
Potential Energy = mass x acceleration due to gravity x height
In this case, the mass of the flask doesn't affect its potential energy, so we can neglect it. The acceleration due to gravity is approximately 9.8 m/s^2. The height at which the flask is held is 1.75 meters.
Potential Energy = 1.75 meters x 9.8 m/s^2 = 17.15 Joules
Now, let's consider the impact force on the flask when it hits the ground. To calculate this, we can use the principle of conservation of energy. The potential energy of the flask is converted into kinetic energy when it falls. The kinetic energy is given by the formula:
Kinetic Energy = 0.5 x mass x velocity^2
Since the flask is dropped, its initial velocity is 0. The final kinetic energy is equal to the potential energy before it was dropped.
Potential Energy = Kinetic Energy
17.15 Joules = 0.5 x mass x velocity^2
We don't know the mass of the flask, but it cancels out on both sides of the equation. Therefore, we are left with:
17.15 = 0.5 x velocity^2
Solving for velocity:
velocity^2 = 34.3
velocity ≈ √34.3
velocity ≈ 5.85 m/s
Now, we need to consider the time it takes for the flask to reach the ground. We can use the equation of motion:
Distance = initial velocity x time + 0.5 x acceleration x time^2
The initial velocity is 0, as the flask is dropped from rest. The distance is the height at which the flask was dropped, which is 1.75 meters. The acceleration is due to gravity, -9.8 m/s^2.
1.75 = 0.5 x (-9.8) x time^2
Solving for time:
time^2 = -1.75 / (-4.9)
time^2 ≈ 0.357
time ≈ √0.357
time ≈ 0.598 seconds
Therefore, it would take approximately 0.598 seconds for the flask to break all over the student's sneakers after it is dropped.