A salami sandwich is dropped from the top of a 37 m tall construction crane. What is the speed of the sandwich when it is halfway to the ground?
(Use conservation of energy!)
Ek + Ep = mg*37.
Ek + mg*18.5 = mg*37
Ek = mg*37 - mg*18.5 = mg*18.5
Ek = 0.5m*V^2 = mg*18.5
V^2 = mg*18.5/0.5m = 2g*18.5 = 19.6*18.5
= 363 Joules.
V = 19 m/s.
Ek = Kinetic energy.
Ep = Potential energy.
Correction
V^2 = 363 (m/s)^2. NOT 363 Joules.
To find the speed of the sandwich when it is halfway to the ground, we can use the principle of conservation of energy. According to this principle, the initial potential energy of the sandwich at the top of the crane is converted entirely into kinetic energy when it reaches the halfway point.
First, let's find the potential energy of the sandwich at the top of the crane. The potential energy of an object can be calculated using the formula:
Potential energy = mass × gravitational acceleration × height
Given that the height of the crane is 37 m and let's assume the mass of the sandwich is 0.2 kg, and the gravitational acceleration is approximately 9.8 m/s^2, we can calculate the potential energy:
Potential energy = 0.2 kg × 9.8 m/s^2 × 37 m = 72.68 J
Since energy is conserved, this potential energy at the top is converted entirely into kinetic energy when the sandwich is halfway to the ground.
The kinetic energy of an object can be calculated using the formula:
Kinetic energy = 0.5 × mass × velocity^2
At the halfway point, the kinetic energy will be equal to the potential energy.
Therefore, we can set up the equation:
0.5 × mass × velocity^2 = potential energy
Plugging in the values, we have:
0.5 × 0.2 kg × velocity^2 = 72.68 J
Simplifying the equation, we get:
0.1 kg × velocity^2 = 72.68 J
Now we can solve for the velocity. Dividing both sides by 0.1 kg, we get:
velocity^2 = 72.68 J / 0.1 kg
velocity^2 = 726.8 m^2/s^2
Taking the square root of both sides, we get:
velocity = √(726.8 m^2/s^2)
Calculating the square root, we find:
velocity ≈ 26.98 m/s
Therefore, the speed of the sandwich when it is halfway to the ground is approximately 26.98 m/s.