4.4.1 Understanding Conservation of Mechanical Energy Flashcards
Understanding Conservation of Mechanical Energy
- If there are only conservative forces acting on a system, then its mechanical energy is conserved: E mechanical= K+ U=constant.
- In many situations, especially those with complicated force diagrams, conservation of mechanical energy is a powerful tool for understanding the behavior of the system.
- Conservation of mechanical energy can be derived from the definitions of kinetic and potential energy and the work-kinetic energy theorem.
True or false?
A pendulum is lifted at a 15° angle with respect to the vertical and released from rest (see diagram). When the pendulum swings through the air and returns to its starting point, it only makes a 14° angle. In this one instance, conservation of mechanical energy was violated.
false
Using the points numbered on the succession of positions on the diagram, state which of the following is not correct for the type of energy the pogo stick has at that moment. We are considering an ideal world with no type of friction. Treat the system as being comprised of the pogo stick and the boy.
Point 3: some kinetic energy and some elastic potential energy
A nonlinear spring produces a conservative force described by F(x) = -k1x^2 - k2x, where k1 and k2 are positive constants. Which of the following is the change in potential energy of such a spring, if it is extended from x = 1m to x = 2m
(7/3) k1 + (3/2) k2
True or false?
You and a friend are discussing the design of a roller coaster that has minimal friction. Your friend states that each successive hill of the roller coaster must be shorter than the preceding hills in order for the roller-coaster car to make it all the way around the ride, but you argue that it doesn’t matter what the heights of the hills are as long as the first hill is the highest. Your friend is not correct.
true
A roller-coaster car starts off at rest on top of a hill with a height of 40 m. Its initial gravitational potential energy is 10,000 J. After the car has moved down the hill and then up to the top of a loop only 20 m high, which of the following is its total energy? Assume that friction is negligible.
10,000 J
Which of the following statements most correctly defines the conservation of mechanical energy ?
If all the energy of a system is in the form of kinetic and potential energy and has a conservative force acting on it, the sum of the potential and kinetic energies at any moment is constant.
A diver starts on a 20 m tower. His total potential energy is 10,000 J. After jumping off the tower toward a pool of water, which of the following is the diver’s potential energy at the heights of 15 m, 10 m, and 2 m, respectively? Ignore any air resistance.
7,500 J; 5,000 J; 1,000 J
A girl is on the roof of a building and drops a tennis ball. At the same time, a boy on the ground, right below the girl, throws an identical tennis ball straight up in the air. Ignore all forms of friction. The two balls are side by side at the point at which the boy’s ball is highest above the ground. Which ball will land on the ground first?
The girl’s ball lands first.
True or false?
If there is negligible friction between a roller-coaster and the track as well as with the air, the roller-coaster car must start at a position higher than the top of the loop if it wants to make it all the way around the loop.
true
