Week 6 โ Power, non-conservative forces, and more
Power measures how fast work is done:
A 100-hp engine can do the same work as a 10-hp engine, but 10 times faster. That's why race cars have high horsepower!
1 hp = 746 W (mechanical horsepower)
1 kW = 1000 W
A 70-kg person climbs 10 m of stairs in 8 seconds. What is their power output?
Step 1 โ Work done:
Step 2 โ Power:
โ Power output โ 858 W (about 1.2 horsepower)
When friction or air resistance is present, mechanical energy is NOT conserved โ some energy "escapes" as heat:
Where Wnc is the work done by non-conservative forces (usually negative, removing energy).
A 5-kg block slides at 8 m/s across a rough floor (ฮผk = 0.3). How far does it travel before stopping?
Step 1 โ Initial KE:
Step 2 โ Work by friction:
Step 3 โ Energy conservation:
โ Distance = 10.9 m
| Type | Example | Work Reversible? |
|---|---|---|
| Conservative | Gravity, spring force, electrostatic | Yes โ energy stored as PE |
| Non-conservative | Friction, air resistance, tension in rope with motor | No โ energy dissipated as heat |
Problem 1: A motor lifts a 200-kg load 10 m in 5 seconds. What is the power output? (Assume constant speed.)
Problem 2: A 3-kg block slides at 6 m/s on a surface with ฮผk = 0.4. How far does it slide before stopping?
Problem 3: A 0.5-kg ball is thrown upward at 12 m/s. Ignoring air resistance, what is its kinetic energy at the top of its path?
Q1: Is the work done by friction positive, negative, or zero? Why?
Negative. Friction always opposes motion (ฮธ = 180ยฐ, cos 180ยฐ = โ1), so W = Fdยทcos(180ยฐ) = โFd. It removes energy from the system.
Q2 (mini-problem): A 10-kg sled slides from rest down a 15-m hill (height 8 m). At the bottom, its speed is 10 m/s. How much energy was lost to friction?
Initial PE = mgh = 10 ร 9.8 ร 8 = 784 J
Final KE = ยฝ(10)(10ยฒ) = 500 J
Energy lost = 784 โ 500 = 284 J (to friction)