1. If a brick is being held (stationary) 15 m above the ground the potential energy will be equal to the total energy of the system.
True
False
2. If a brick is being held (stationary) 15 m above the ground and then dropped, the kinetic energy will be equal to the total energy of the system when the brick has fallen 5 m.
True
False
3. A roller coaster car will have the same total energy at the top of the ride as it does when it just reaches the bottom.
True
False
4. A change in mass will have a greater affect on the kinetic energy of an object then a change in velocity.
True
False
1. False: The potential energy of the brick is part of the total energy of the system, but it is not equal to the total energy. The total energy of a system includes both the potential energy and the kinetic energy.
To calculate the total energy of the system, you need to add the potential energy and the kinetic energy together. The potential energy of the brick can be calculated using the formula PE = mgh, where m is the mass of the brick, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height of the brick above the ground.
The kinetic energy of the brick can be calculated using the formula KE = 0.5mv^2, where m is the mass of the brick and v is the velocity of the brick. If the brick is stationary, its velocity is 0, so the kinetic energy will be 0.
Therefore, the total energy of the system is equal to the potential energy in this case.
2. False: The kinetic energy of the brick will not be equal to the total energy of the system when the brick has fallen 5 m. The total energy of the system remains constant throughout the fall, but the distribution between potential and kinetic energy changes.
Initially, when the brick is held stationary 15 m above the ground, it only has potential energy. As it falls, some of the potential energy is converted into kinetic energy. At any point during the fall, the total energy (potential energy + kinetic energy) will be the same as the initial total energy. However, the specific amounts of potential and kinetic energy will be different.
To calculate the kinetic energy of the brick when it has fallen 5 m, you would need to know its velocity at that point. The kinetic energy can be calculated using the formula KE = 0.5mv^2, where m is the mass of the brick and v is its velocity.
3. False: The roller coaster car does not have the same total energy at the top of the ride as it does when it just reaches the bottom. The total energy of the system changes as the car moves along the track.
At the top of the ride, the car has a combination of potential and kinetic energy. As it goes down the track, the potential energy decreases while the kinetic energy increases. By the time it reaches the bottom, all of the potential energy is converted into kinetic energy.
Therefore, the total energy at the top of the ride is higher than the total energy at the bottom.
4. False: A change in velocity will have a greater effect on the kinetic energy of an object than a change in mass. The kinetic energy depends on both mass and velocity, but its dependence on velocity is quadratic while its dependence on mass is linear.
The kinetic energy can be calculated using the formula KE = 0.5mv^2, where m is the mass of the object and v is its velocity. As you can see, the velocity is squared, whereas the mass is not. This means that a change in velocity will have a greater impact on the kinetic energy compared to a change in mass.
For example, doubling the velocity of an object will result in the kinetic energy increasing by a factor of four (2^2), while doubling the mass will only result in the kinetic energy doubling.
Therefore, a change in velocity has a greater effect on the kinetic energy of an object compared to a change in mass.