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 calculate the total amount of water ejected per second and then use the formula for force to determine the backward force.
First, let's find the volume of water ejected per second. We are given that the hose ejects 5*10^-4 m^3 of water per second.
Next, let's find the volume of water ejected through the mouth of the hose per second. The area of the mouth of the hose is given as 5 cm^2, which is equal to 5*10^-4 m^2 (since 1 cm = 0.01 m).
Now, multiply the volume of water ejected through the hose (5*10^-4 m^3/sec) by the inverse of the mouth area (1 / 5*10^-4 m^2) to find the volume of water ejected per second through the mouth of the hose.
(5*10^-4 m^3/sec) * (1 / 5*10^-4 m^2) = 1 m/sec
Therefore, the volume of water ejected per second through the mouth of the hose is 1 m^3/sec.
Now we can calculate the mass of the water ejected per second. The density of water is given as 10^3 kg/m^3. The density of an object is the ratio of its mass to its volume, so we can rearrange the equation to solve for mass.
Density = Mass / Volume
Mass = Density * Volume
Mass = (10^3 kg/m^3) * (1 m^3/sec) = 10^3 kg/sec
Finally, we can calculate the backward force exerted on the gardener using Newton's second law of motion (force = mass * acceleration). Since the water is being ejected in the backward direction, the force exerted on the gardener will be equal to the mass of water ejected per second multiplied by its acceleration in the backward direction.
The acceleration can be calculated using the rate of change of momentum. Since the momentum change is equal to the mass of water ejected per second multiplied by the change in velocity, the acceleration is equal to the change in velocity divided by the time taken, which is 1 second in this case.
Acceleration = Change in velocity / Time taken
Acceleration = (0 - 0) m/sec / 1 sec = 0 m/sec^2
Now, we can calculate the backward force exerted on the gardener.
Force = Mass * Acceleration
Force = 10^3 kg/sec * 0 m/sec^2 = 0 N
Therefore, the backward force exerted on the gardener is 0 Newtons.