A gardener waters a lawn. the hose ejects 5*10^-4 m^3 of water per second. The area of the mouth of the hose is 5 cm^2. Find the backward force exerted on the gardener.[density of water=10^3kg/m^3]
To find the backward force exerted on the gardener, we need to determine the speed at which the water is ejected from the hose. We can then use Newton's second law of motion (F = ma) to calculate the force.
First, let's convert the area of the hose mouth from square centimeters to square meters. Since 1 m = 100 cm, we have:
Area (m^2) = (5 cm^2) * (1 m^2 / 10000 cm^2)
Area = 5 * 10^-4 m^2
Next, we need to calculate the speed of the water. We know that the volume of water ejected per second is 5 * 10^-4 m^3. Assuming the water flows uniformly through the hose, we can use the equation:
Speed (m/s) = Volume (m^3) / Area (m^2)
Speed = (5 * 10^-4 m^3) / (5 * 10^-4 m^2)
Speed = 1 m/s
Now, we can use Newton's second law to calculate the force:
F = m * a
The mass (m) of the water can be determined using the density of water:
Mass (kg) = Density (kg/m^3) * Volume (m^3)
Mass = (10^3 kg/m^3) * (5 * 10^-4 m^3)
Mass = 0.5 kg
Now we can calculate the force:
F = (0.5 kg) * (1 m/s)
F = 0.5 N
Therefore, the backward force exerted on the gardener is 0.5 Newtons.