You decide to use your garden hose to wash your garage door. The water shoots out at a rate of 10 kg/s and a speed of 16 m/s with respect to the hose. When the water hits the garage, its speed decreases to zero. Determine the force that the water exerts on the wall. What assumptions did you make?
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To determine the force that the water exerts on the wall, we can use Newton's second law of motion, which states that force (F) is equal to the change in momentum (Δp) per unit time (Δt). In equation form, this can be written as:
F = Δp / Δt
To find the change in momentum (Δp), we need to first calculate the initial momentum (p_initial) of the water as it leaves the hose and the final momentum (p_final) of the water when it hits the garage.
The initial momentum (p_initial) is given by the product of the mass (m) and the initial velocity (v_initial):
p_initial = m * v_initial
Here, the mass of the water is 10 kg/s (given) and the initial velocity with respect to the hose is 16 m/s (given).
Next, let's calculate the final momentum (p_final) of the water when it hits the garage. Since the speed decreases to zero, the final momentum will be zero:
p_final = 0
Now, we can determine the change in momentum (Δp) by subtracting the final momentum from the initial momentum:
Δp = p_final - p_initial
= 0 - (m * v_initial)
Finally, we need to determine the time interval (Δt) over which the change in momentum occurs. Since the question does not provide any information about this time interval, we assume that the change in momentum happens instantaneously. Therefore, we can consider it as a delta function, which means Δt is infinitesimally small.
Substituting the values into the equation for force, we have:
F = Δp / Δt
= (0 - (m * v_initial)) / Δt
≈ - (m * v_initial) / Δt
In this case, we can assume that the force exerted by the water on the wall is a single instantaneous impulse. The negative sign indicates that the force is directed towards the opposite direction of motion, which represents the water hitting the garage.
Assumptions made:
1. The change in momentum occurs instantaneously.
2. The force exerted by the water on the wall is a single instantaneous impulse.