Here's a set of physics problems to challenge your knowledge of the concepts of energy and motion. Very few have come up with correct answer to all these problems (question 2 in particular) and I've asked some very smart Maths and Physics phDs! The maths isn't that hard but you have to be very careful about what equations you use and what assumptions you make
Bonus questions are included that any good A-Level physicist should be able to answer but are not part of the main theme to these questions and are arguably not as hard. Usual assumptions can be made in these questions. Partial marks are given for estimates to answers!
- Assume g = 10 and is constant
- This is NOT a trick question!!! It is all pure and simple physics
- Assume Earth is flat
Alice, who weighs 100kg, steadly climbs a ladder at a constant velocity to a height of 10 meters and reaches the top after 100 seconds.
Question: What is the minimum energy needed for Alice to do this?
Bonus: What is the person's power output?
Bob, who also weighs 100kg, straps a rocket pack to his back and follows Alice as she climbs the ladder. That is, Bob also climbs through the air at constant velocity to 10 meters and reachers the top after 100 second.
For this problem, you can assume the mass of the jet fuel consumed is relatively small compared to the mass of Bob. However, if you feel it helps your calculations, you can assume that this is a pie powered jet pack. In 1) Alice eats a 1kg pie before starting uses up all that pie power to climb the lader. Similarly in 2) Bob puts the 1kg pie into his jet pack and uses it all up to get to the top
Question: What is the minimum energy needed for Bob to do this?
Question: Does the energy used in both cases depend on the time taken in getting to the top? If not, why not? If so, by how much?
3) (Bonus problem)
Cain, who also weighs 100kg, puts himself into a human cannon and fires himself up into the air, just reaching the 10 meter height Question: What is the minimum energy needed from the cannon to do this? Bonus: How fast was Cain initially travelling as he left the cannon?
- Everyone is infinitely short
- Bob's jet fuel is as light as you like and produces no heat
- There is no air friction
- ... other usual assumptions?
For answers, email kevin at glorat dot net!