This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify the given values and relevant physical constants. The speed of the water stream is v = 15 ms^-1. The cross-sectional area of the tube is A = 10^-2 m^2. The density of water is = 1000 kg m^-3. The problem states that the water does not rebound, meaning its final velocity after impact is 0 ms^-1. Step 2: Determine the formula for the force exerted by a fluid stream. The force exerted by a fluid stream on a surface is equal to the rate of change of momentum of the fluid. Since the water does not rebound, its final momentum is zero. The mass of water hitting the wall per unit time (mass flow rate) is given by (dm)/(dt) = A v. The initial momentum per unit time is (d(mv))/(dt) = v (dm)/(dt). Since the final velocity is zero, the change in momentum per unit time (which is the force) is: F = d(momentum)dt = (d(mv))/(dt) = v ((dm)/(dt)) Substitute the expression for mass flow rate: F = v ( A v) = A v^2 Step 3: Substitute the values into the formula and calculate the force. F = (1000 kg m^-3) × (10^-2 m^2) × (15 ms^-1)^2 F = 1000 × 0.01 × 225 F = 10 × 225 F = 2250 N Step 4: Compare the calculated force with the given options. The calculated force is 2250 N, which matches option (4). The final answer is 2250 N. Send me the next one 📸