A water jet strikes a stationary vertical plate horizontally at a rate of 5 kg/s with a velocity of 35 km/h. Assume the water stream moves in the vertical direction after the strike. What is the magnitude (absolute value) of the force needed to prevent the plate from moving horizontally? Express your answer in N.
Question
A water jet strikes a stationary vertical plate horizontally at a rate of 5 kg/s with a velocity of 35 km/h. Assume the water stream moves in the vertical direction after the strike. What is the magnitude (absolute value) of the force needed to prevent the plate from moving horizontally? Express your answer in N.
Solution
Step 1: Convert the velocity of the water jet from km/h to m/s. There are 1000 meters in a kilometer and 3600 seconds in an hour, so:
35 km/h * (1000 m / 1 km) * (1 h / 3600 s) = 9.72 m/s
Step 2: The force exerted by the water jet on the plate can be calculated using the formula for the change in momentum per unit time, which is also the definition of force (F = Δp/Δt). In this case, the change in momentum is the mass of the water jet times its velocity, and the change in time is 1 second (since the rate of the water jet is given in kg/s).
F = Δp/Δt = m * v / t
Step 3: Substitute the given values into the equation:
F = (5 kg/s) * (9.72 m/s) / 1 s = 48.6 N
So, the magnitude of the force needed to prevent the plate from moving horizontally is approximately 48.6 N.
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