HW10.43 -- 3 Ways to Solve: Energy & Springs
The circus has hired you to design a spring-launched roller coaster that will carry up to two passengers per car. The car goes
up a 15-m-high hill, then
descends 20 m to the track's lowest point. You've determined that the
spring can be
compressed a maximum of
2.0 m and that a loaded
car will have a maximum
mass of
400 kg . For safety reasons, the spring constant should be
20% larger than the minimum needed for the car to just make it over the top. (Note that all data is given to 2-sig figs)
(a) What
spring constant should you specify?
(b) What is the
maximum speed of a
350 kg car if the spring is compressed the full amount?
- Picture
- System & Assumptions
- Decision of solution method: Newton's Laws or Energy Method
- IF Newton; Free Body Diagram (including Fnet, show coordinate system)
- IF Energy: Before and After Diagram
- Solve
- Assess
Key Ideas
| $$ \mathbf { \vec a } (t) = { { \mathbf { \vec F }(t) \over m } } \rightarrow \,$$
| $$ \Delta \mathbf { \vec v } = \int { { \mathbf { \vec F }(t) \over m }\, dt } \,$$ |
$$ \Delta \mathbf { \vec p } = \int { { \mathbf { \vec F }(t) }\, dt }
\equiv \mathbf { \vec J } \, $$ |
Momentum is based on Newton's 2nd and 3rd Laws (not new physics)
Advantage (優點): Simplifies solutions when only final state required.
Disadvantage (缺點): Loose all time information
isolated system → Δ p = 0 (Momentum Conservation)
PHeT Sim Introduction
Lecture Knight vs4 Chapter 11
