Which falling object will result in the least kinetic energy when it collides with the ground?
a
100 grams of water falling at 10 m/s
b
10 grams of water falling at 1 m/s
c
10 grams of dirt falling at 2 m/s
d
100 grams of dirt falling at 15 m/s
We can find the kinetic energy using the formula: KE = (1/2)mv^2
where KE is the kinetic energy, m is the mass, and v is the velocity.
a: KE = 0.5 * 100g * (10 m/s)^2 = 0.5 * 100 * 100 = 5000 J (joules)
b: KE = 0.5 * 10g * (1 m/s)^2 = 0.5 * 10 * 1 = 5 J
c: KE = 0.5 * 10g * (2 m/s)^2 = 0.5 * 10 * 4 = 20 J
d: KE = 0.5 * 100g * (15 m/s)^2 = 0.5 * 100 * 225 = 11250 J
The least kinetic energy is generated by option b, which is 10 grams of water falling at 1 m/s.
Which falling object will result in the least kinetic energy when it collides with the ground?
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1 point
100 grams of dirt falling at 15 m/s
10 grams of dirt falling at 2 m/s
100 grams of water falling at 10 m/s
10 grams of water falling at 1 m/s
The least kinetic energy will be generated by the option: 10 grams of water falling at 1 m/s.
Four rivers have the same volume of water flow over time but fall from different heights to power hydroelectric dams. Which dam would provide the most hydroelectric power?
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1 point
dam C: fall height of 135 feet
dam B: fall height of 75 feet
dam A: fall height of 175 feet
dam D: fall height of 100 feet
The hydroelectric power generated by a dam is given by the formula: P = ρghQ
where P is the power, ρ is the density of water, g is acceleration due to gravity, h is the fall height and Q is the volume flow rate.
Since all four rivers have the same volume flow rate, we can ignore the Q variable.
Let's assume the density of water is 1000 kg/m³ and acceleration due to gravity is 9.81 m/s²
a: P = 1000 * 9.81 * 175 = 1,725,750 W
b: P = 1000 * 9.81 * 75 = 735,525 W
c: P = 1000 * 9.81 * 135 = 1,328,925 W
d: P = 1000 * 9.81 * 100 = 981,000 W
Therefore, dam A with a fall height of 175 feet would provide the most hydroelectric power.