A feather and a bowling ball are each dropped from an equal height in a vacuum and land at the same time. Which graph shows the total mechanical energy of the bowling ball as it falls?
a
bd88da29-8af3-429f-8a9a-cee09d46a4d9.PNG
b
a5f778d3-7724-4359-bdf6-fd6add5e6583.PNG
c
c428af47-7e5d-429b-8a37-45cce7c6de87.PNG
d
a4b0346b-6c69-4eaa-b58a-c1b98dc60604.PNG
a
The correct answer is (c) c428af47-7e5d-429b-8a37-45cce7c6de87.PNG.
To determine which graph shows the total mechanical energy of the bowling ball as it falls, we need to understand the concept of mechanical energy.
Mechanical energy can be divided into two parts: kinetic energy and potential energy.
1. Kinetic energy (KE) is the energy of an object due to its motion and is given by the equation KE = (1/2)mv^2, where m represents the mass of the object and v represents its velocity.
2. Potential energy (PE) is the energy an object possesses due to its position or state and can be further divided into gravitational potential energy (PEg) and elastic potential energy (PEe). For this scenario, we will only consider gravitational potential energy.
When an object falls, its potential energy decreases while its kinetic energy increases, maintaining the total mechanical energy constant. As a result, the sum of kinetic energy and potential energy remains the same throughout the fall.
Now, let's analyze the given graphs:
a. This graph shows a continuous decrease in total mechanical energy, which is not consistent with the conservation of mechanical energy. Therefore, graph a does not depict the total mechanical energy of the bowling ball as it falls.
b. This graph shows a constant total mechanical energy, where kinetic energy is continuously increasing, compensating for the decrease in potential energy. This is consistent with the conservation of mechanical energy, so graph b could represent the total mechanical energy of the bowling ball as it falls.
c. This graph shows an increasing total mechanical energy, which is not possible since mechanical energy is conserved during free fall. Therefore, graph c does not represent the total mechanical energy of the bowling ball as it falls.
d. This graph shows a decreasing total mechanical energy, similar to graph a. Since mechanical energy should be conserved, we can conclude that graph d does not show the total mechanical energy of the bowling ball as it falls.
Based on our analysis, the graph that shows the total mechanical energy of the bowling ball as it falls is option b.