ENERGY UNIT TEST
Name:________
Energy
Work & Power
Kinetic Energy & GPE
1
𝐸𝑘 = 𝑚𝑣 2
2
𝑊 = 𝐹⃑ ∙ ∆𝑑⃑ = 𝐹∆𝑑⃑𝑐𝑜𝑠𝜃
𝐸𝑓𝑓 = (
𝑊 ∆𝐸
=
𝑡
𝑡
∆𝐸𝑔 = 𝑚𝑔∆ℎ
𝐸𝑡ℎ
𝑚
𝐸𝑡𝑜𝑡𝑎𝑙, 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 = 𝐸𝑡𝑜𝑡𝑎𝑙, 𝑓𝑖𝑛𝑎𝑙
𝐿𝑣 =
𝐸𝑡ℎ
𝑚
𝐸𝑜𝑢𝑡𝑝𝑢𝑡
) × 100%
𝐸𝑖𝑛𝑝𝑢𝑡
𝐸𝑡ℎ = 𝐹𝑓 ∆𝑑 (friction)
Forces
Pendulum
𝐹⃑𝑛𝑒𝑡 = 𝑚𝑎⃑, 𝐹⃑𝑛𝑒𝑡 = 𝐹⃑1 + 𝐹⃑2 + 𝐹⃑3 + ⋯
𝐿
𝑇 = 2𝜋√
𝑔
𝑚
𝐹⃑𝑔 = 𝑚𝑔⃑ where 𝑔⃑ = 9.8 2 [𝑑𝑜𝑤𝑛]
Constant Velocity
𝑣⃑𝑎𝑣
1
𝐸𝑒 = 𝑘∆𝑥 2
2
Simple Harmonic Motion
Mass on a Spring
𝑚
𝑇 = 2𝜋√
𝑘
𝑣⃑ =
𝐸𝑡ℎ = 𝑚𝑐∆𝑇
𝐿𝑓 =
𝑊 = ∆𝐸
𝑃=
Thermal Energy
∆𝑑⃑
∆t
𝑣⃑1 + 𝑣⃑2
=
2
𝑠
𝐹𝐹 = 𝜇𝐹𝑁
𝐹⃑𝑠 = 𝑘∆𝑥⃑
Constant Acceleration
𝑣⃑2 = 𝑣⃑1 + 𝑎⃑∆t
𝑣⃑1 + 𝑣⃑2
∆𝑑⃑ = (
) ∆t
2
1
∆𝑑⃑ = 𝑣⃑1 ∆t + 𝑎⃑∆𝑡 2
2
1
∆𝑑⃑ = 𝑣⃑2 ∆t − 𝑎⃑∆𝑡 2
2
𝑣⃑22 = 𝑣⃑12 + 2𝑎⃑∆𝑑⃑
WORK:
Q1. A 250 kg beam is raised through 25 m at a constant velocity by a crane.
a) Draw an FBD for the beam.
b) Determine the work done by the crane on the beam.
c) Determine the work done by gravity on the beam.
POWER:
Q2. An electric car can accelerate from rest to 96.5 km/h (this is often called
“from 0 to 60” measured in miles per hour) in 2.4 s. Find the power of the car,
given its mass of 1961 kg.
Kinetic Energy:
Q3. An 18 kg curling rock is pushed with a constant force of 13.0 N. The
curling rock has an initial speed of 1.5 m/s. Assuming there is no friction,
determine the speed of the rock after it has travelled 2.1 m.
Gravitational Potential Energy:
Q4. How much gravitational potential energy do you gain when you walk up
the CN Tower stairs (346 m)?
What type of energy/energies transformed into GPE in this scenario?
Conservation of Energy:
Q5. A student is swinging a 200 g yo-yo on a 1.0 m long string. How fast must
the yo-yo be moving at the bottom of the circle to reach the top of the circle
with no speed?
EFFICIENCY:
Q6. A glow-worm can use bioluminescence to
transform 2.1 J of chemical energy into 1.6 J of
radiant energy. What is the efficiency of the
glow-worm?
Specific Heat Capacity Values for Common Substances
Substance
J/kg°C
or J/kgK
Substance
J/kg°C
or J/kgK
Water
4186
Silver
236
Ice
2093
Mercury
138
Steam
2009
Gold
130
Methyl Alcohol
2549
Lead
128
Ethyl Alcohol
240
Brass
380
Benzene
1750
Iron
460
Soil
1046
Steel
452
Air (dry)
1005
Copper
387
Liquid Nitrogen
110
Aluminum
900
Glass
837
Sand
800
Q7. How much thermal energy needs to be added to 0.455 kg benzene to
heat it from 20.2°C to 31.4°C?
LATENT HEAT:
Q8. Determine how much mass of ice at -5°C could be converted to water
vapor at 125°C given 1 million joules of energy?
Lf water = 3.3x105 J/Kg
Lv water = 2.3 x106 J/Kg