A \(2.0\)-kg block slides from rest down a frictionless ramp of height \(5.0\) m, then slides on a rough horizontal surface (\( \mu_k = 0.20 \)) until it stops. How far does it travel on the horizontal surface?
Answer: m
Solution:
At bottom of ramp: \( E_k = mgh = 2.0(9.8)(5.0) = 98 \) J
Friction does work: \( W_f = f_k d = \mu_k mg d = 0.20(2.0)(9.8)d = 3.92d \)
Set \( 3.92d = 98 \) → \( d = 25 \) m
Q9 — STSE (concept)
Which Ontario electricity source has the highest typical efficiency at converting input energy to electrical output?
Solution:
Hydroelectric plants achieve about 85–90% efficiency because gravitational PE of water is converted directly to mechanical and then electrical energy with relatively few thermal losses.
Q10 — Calorimetry (heat exchange)
A \(0.20\)-kg block of metal at \(100°\)C is dropped into \(0.30\) kg of water at \(20°\)C. Final temperature is \(28°\)C. Calculate the specific heat capacity of the metal. (\( c_\text{water}=4186 \) J/(kg·°C))
Answer: J/(kg·°C)
Solution:
Heat lost by metal = heat gained by water:
\( m_M c_M (100-28) = m_W c_W (28-20) \)
\( 0.20 c_M (72) = 0.30(4186)(8) \)
\( 14.4 c_M = 10046 \) → \( c_M = 698 \) J/(kg·°C)