A student drops the same 10 kilogram ball from heights of one, two, and three meters. Which bar graph accurately shows the ball’s kinetic energy when dropped from each height?
a
A
b
B
c
C
d
D
The correct bar graph would be option C.
Unfortunately, I am unable to see the bar graphs you mentioned. However, I can explain how to determine the kinetic energy of the ball at each height.
The kinetic energy (KE) of an object is given by the equation:
KE = 1/2 * m * v^2
Where m is the mass of the ball and v is its velocity. When the ball is dropped, it only has gravitational potential energy (PE), given by:
PE = m * g * h
Where g is the acceleration due to gravity (approximately 9.8 m/s^2) and h is the height from which the ball is dropped.
As the ball falls, its potential energy is converted into kinetic energy. The velocity of the ball just before it hits the ground can be calculated using the equation:
v = sqrt(2 * g * h)
Substituting this expression for v back into the equation for KE, we get:
KE = 1/2 * m * (sqrt(2 * g * h))^2
= 1/2 * m * 2 * g * h
= m * g * h
Therefore, the kinetic energy of the ball when dropped from different heights is directly proportional to the height. In other words, the ball will have the same kinetic energy when dropped from the same mass but different heights.
To determine which bar graph accurately represents the ball's kinetic energy when dropped from each height, we need to understand the equation for kinetic energy.
Kinetic energy is given by the equation KE = (1/2) * m * v^2, where KE represents kinetic energy, m represents mass, and v represents velocity.
In this case, the mass of the ball is 10 kilograms, and we need to find the kinetic energy when dropped from heights of one, two, and three meters.
To find the velocity, we can use the equation v = √(2 * g * h), where g represents the acceleration due to gravity (approximately 9.8 m/s^2) and h represents the height from which the ball is dropped.
For the height of one meter, the velocity would be v = √(2 * 9.8 * 1) ≈ 4.43 m/s.
For the height of two meters, the velocity would be v = √(2 * 9.8 * 2) ≈ 6.26 m/s.
For the height of three meters, the velocity would be v = √(2 * 9.8 * 3) ≈ 7.67 m/s.
Now that we have the velocities, we can calculate the kinetic energies for each height using the formula KE = (1/2) * m * v^2.
For the height of one meter, the kinetic energy would be KE = (1/2) * 10 * (4.43)^2 ≈ 97.76 J.
For the height of two meters, the kinetic energy would be KE = (1/2) * 10 * (6.26)^2 ≈ 196.25 J.
For the height of three meters, the kinetic energy would be KE = (1/2) * 10 * (7.67)^2 ≈ 370.87 J.
Now that we have calculated the kinetic energies, we can identify the correct bar graph by comparing the values. The bar graph that accurately represents the ball's kinetic energy when dropped from each height should have a bar at approximately 97.76 J for one meter, 196.25 J for two meters, and 370.87 J for three meters.
Looking at the options provided:
a) A
b) B
c) C
d) D
We need to visually compare the values on the graph bars to the calculated kinetic energies. Once you have determined which bar graph matches the calculated values within a reasonable range, you can identify the correct answer.
Note: Without seeing the actual bar graphs, it is not possible to provide a definitive answer. You would need to compare the values on the bar graph with the calculated kinetic energies to determine the accurate representation.