Which of these energies might correspond to the KE of a person riding a bicycle on a road? 10 J; 1 kJ; 100kJ
KE is 1/2 mv^2. Take your mass (weight in lbs/2.2), divide by two, take a typical speed say 10mi/hr or 6.6km/hr or 5m/s, square it, and do the math.
10 J
To calculate the kinetic energy (KE) of a person riding a bicycle on a road, we can use the equation KE = 1/2 mv^2, where m is the mass of the person and v is the velocity of the person.
Let's assume the mass of the person riding the bicycle is 70 kg (154 lbs) and the velocity is 5 m/s. We will use these values to calculate the KE.
1. Convert the mass from pounds to kilograms:
mass = 154 lbs ÷ 2.2 = 70 kg
2. Calculate the kinetic energy:
KE = 1/2 × mass × velocity^2
KE = 1/2 × 70 kg × (5 m/s)^2
KE = 1/2 × 70 kg × 25 m^2/s^2
KE = 875 Joules (J)
So, the kinetic energy of a person riding a bicycle on a road would correspond to 875 J.
Out of the given options:
- 10 J: This is much lower than the calculated kinetic energy.
- 1 kJ (1 kilojoule = 1000 J): This is higher than the calculated kinetic energy.
- 100 kJ (100 kilojoules = 100,000 J): This is significantly higher than the calculated kinetic energy.
Therefore, the most appropriate option that corresponds to the KE of a person riding a bicycle on a road is 10 J.
To determine the kinetic energy (KE) of a person riding a bicycle on a road, we can use the formula KE = 1/2 * m * v^2, where m is the mass of the person and v is the velocity or speed at which they are riding.
First, we need to find the mass of the person in kilograms. To do this, we can convert their weight from pounds to kilograms. Divide the weight of the person in pounds by 2.2 to get their mass in kilograms.
Next, we need to choose a typical speed at which the person is riding. Let's say they are riding at 10 miles per hour (mph), 6.6 kilometers per hour (km/hr), or 5 meters per second (m/s).
Let's go through the calculations step by step using the given speeds:
1. For 10 miles per hour (mph):
- Convert the speed to meters per second (m/s):
10 mph = 10 * 1609.34 m / 3600 s ≈ 4.47 m/s
- Square the speed:
v^2 = (4.47 m/s)^2 ≈ 19.96 m/s^2
- Calculate the kinetic energy:
KE = 1/2 * m * v^2
2. For 6.6 kilometers per hour (km/hr):
- Convert the speed to meters per second (m/s):
6.6 km/hr = 6.6 * 1000 m / 3600 s ≈ 1.83 m/s
- Square the speed:
v^2 = (1.83 m/s)^2 ≈ 3.36 m/s^2
- Calculate the kinetic energy:
KE = 1/2 * m * v^2
3. For 5 meters per second (m/s):
- Square the speed:
v^2 = (5 m/s)^2 = 25 m/s^2
- Calculate the kinetic energy:
KE = 1/2 * m * v^2
Once you have calculated the kinetic energy using the above formulas, compare it to the given energy options of 10 J, 1 kJ, and 100 kJ. Choose the option that is closest to the calculated value.