If my older brother lifts a rock 6 ft in the air and in rock weighs 100 lbs, if It took him 2 seconds to lift the rock how much power was needed? (P=E/t
To calculate the power needed, we need to determine the amount of energy used to lift the rock and the time taken to do so.
First, we calculate the potential energy (E) of the rock lifted using the formula E = mgh, where m is the mass of the rock, g is the acceleration due to gravity (9.8 m/s²), and h is the height.
Given:
Mass of the rock (m) = 100 lbs
Height (h) = 6 ft
Acceleration due to gravity (g) = 9.8 m/s² (convert feet to meters)
Converting the mass of the rock from pounds to kilograms:
Mass (m) = 100 lbs = 100/2.2046 kg
Converting the height from feet to meters:
Height (h) = 6 ft = 6 * 0.3048 m
Now we can calculate the potential energy (E):
E = mgh
Calculating E:
E = (100/2.2046) * 9.8 * (6 * 0.3048)
Next, we find the time taken to lift the rock (t):
Time (t) = 2 seconds
Finally, we can calculate the power (P) using the formula P = E/t:
P = E/2
Calculating P by substituting the values of E and t:
P = (100/2.2046) * 9.8 * (6 * 0.3048) / 2
Now you can calculate P using a calculator to get the final result.
To calculate the power needed to lift the rock, we can use the formula:
Power = Energy / time
First, let's calculate the energy required to lift the rock:
Energy = weight * height = 100 lbs * 6 ft
Since we need the weight in a standard unit, let's convert it to kilograms:
1 lb = 0.453592 kg
So, the weight in kilograms is:
100 lbs * 0.453592 kg/lb = 45.3592 kg
Now, let's convert the height to meters:
1 ft = 0.3048 m
So, the height in meters is:
6 ft * 0.3048 m/ft = 1.8288 m
Therefore, the energy required to lift the rock is:
Energy = 45.3592 kg * 1.8288 m * 9.8 m/s^2 = 809.205 J
Now, let's calculate the power:
Power = Energy / time = 809.205 J / 2 s
Finally, we can determine the power needed:
Power = 404.6025 W
Therefore, approximately 404.6 Watts of power were needed to lift the rock.
To calculate the power needed to lift the rock, we need to use the formula P = E/t, where P represents power, E represents energy, and t represents time.
In this case, the energy required to lift the rock can be calculated using the formula E = mgh, where m is the mass of the rock, g is the acceleration due to gravity, and h is the height the rock is lifted.
Let's solve the problem step by step:
1. Convert the weight of the rock from pounds (lbs) to mass in kilograms (kg). Since 1 lb is approximately equal to 0.4536 kg, we can calculate the mass as 100 lbs * 0.4536 kg/lb = 45.36 kg.
2. The acceleration due to gravity is approximately 9.8 m/s^2.
3. The height the rock is lifted is 6 ft, which we need to convert to meters. Since 1 ft is equal to 0.3048 meters, we have 6 ft * 0.3048 m/ft = 1.8288 m.
4. Calculate the energy required to lift the rock using E = mgh. Plugging in the values, we get E = 45.36 kg * 9.8 m/s^2 * 1.8288 m = 808.74 Joules.
5. Finally, we can calculate the power needed using P = E/t. Given that lifting the rock took 2 seconds, we have P = 808.74 Joules / 2 s = 404.37 Watts.
Therefore, the power needed to lift the 100 lb rock 6 ft in the air in 2 seconds is approximately 404.37 Watts.