student drops the same 10 kilogram bowling ball three separate times. She drops the ball from heights of 1 meter, 2 meters, and 3 meters. Which graph correctly shows the ball’s kinetic energy when dropped from each height?(1 point)
Responses
Sorry, but I can't generate the graphs for you.
To determine the graph that correctly shows the ball's kinetic energy when dropped from each height, we need to understand the relationship between kinetic energy and the height from which the ball is dropped.
The kinetic energy (KE) of an object is given by the equation KE = 1/2 * m * v^2, where m represents the mass of the object and v represents its velocity.
When an object is dropped from a height, it gains velocity as it falls due to acceleration due to gravity. The potential energy (PE) at the initial height is converted into kinetic energy as the object falls.
The velocity of the object can be determined using the equation v = √(2 * g * h), where g represents the acceleration due to gravity and h represents the height from which the object is dropped.
Let's calculate the velocity for each height:
1) When dropped from a height of 1 meter:
v = √(2 * g * h) = √(2 * 9.8 * 1) = √(19.6) ≈ 4.427 m/s (rounded to 3 decimal places)
2) When dropped from a height of 2 meters:
v = √(2 * g * h) = √(2 * 9.8 * 2) = √(39.2) ≈ 6.260 m/s (rounded to 3 decimal places)
3) When dropped from a height of 3 meters:
v = √(2 * g * h) = √(2 * 9.8 * 3) = √(58.8) ≈ 7.675 m/s (rounded to 3 decimal places)
The kinetic energy can now be calculated for each height using the formula KE = 1/2 * m * v^2:
1) KE = 1/2 * 10 * (4.427)^2 ≈ 97.61 J (rounded to 2 decimal places)
2) KE = 1/2 * 10 * (6.260)^2 ≈ 196.60 J (rounded to 2 decimal places)
3) KE = 1/2 * 10 * (7.675)^2 ≈ 294.11 J (rounded to 2 decimal places)
Now, based on these calculations, we can determine which graph correctly shows the ball's kinetic energy when dropped from each height. Unfortunately, without seeing the available graphs, it is not possible to provide a specific response.
Please provide the available graphs, and I will be able to assist you further in identifying the correct one.
To understand which graph correctly shows the ball's kinetic energy when dropped from different heights, we need to understand the concept of kinetic energy and how it is affected by the height of the drop.
Kinetic energy (KE) is the energy an object possesses due to its motion. It is given by the equation KE = 1/2 mv^2, where m is the mass of the object and v is its velocity.
In this case, the mass of the bowling ball is given as 10 kilograms, and it is being dropped from heights of 1 meter, 2 meters, and 3 meters.
When an object is dropped, it gains gravitational potential energy (PE) due to its vertical position above the ground. The amount of potential energy gained is given by PE = mgh, where g is the acceleration due to gravity (approximately 9.8 m/s^2) and h is the height.
As the ball falls, it converts its potential energy into kinetic energy. According to the law of conservation of energy, the total energy (PE + KE) remains constant. Therefore, as potential energy decreases, kinetic energy increases.
Now, let's analyze the height and its effect on kinetic energy for each drop:
- When dropped from a height of 1 meter:
The potential energy gained is PE = mgh = 10 kg * 9.8 m/s^2 * 1 m = 98 Joules. This potential energy will be converted entirely into kinetic energy when the ball reaches the ground.
- When dropped from a height of 2 meters:
The potential energy gained is PE = mgh = 10 kg * 9.8 m/s^2 * 2 m = 196 Joules. Again, this potential energy will be converted entirely into kinetic energy when the ball reaches the ground.
- When dropped from a height of 3 meters:
The potential energy gained is PE = mgh = 10 kg * 9.8 m/s^2 * 3 m = 294 Joules. Once again, this potential energy will be converted entirely into kinetic energy when the ball reaches the ground.
Based on this analysis, the graph that correctly shows the ball's kinetic energy when dropped from each height would have the following relationship:
- Kinetic energy for the 1 meter drop is less than the kinetic energy for the 2 meter drop, but greater than zero.
- Kinetic energy for the 2 meter drop is less than the kinetic energy for the 3 meter drop, but greater than the kinetic energy for the 1 meter drop.
- Kinetic energy for the 3 meter drop is greater than the kinetic energy for both the 1 meter and 2 meter drops.
Without the options for the graphs, I cannot point out a specific graph. However, the correct graph should follow the relationships mentioned above. Remember, the kinetic energy increases as the potential energy decreases with increasing height.