a hose pipe ejects water at a speed of 0.3m/s through a hole of area 50 cm*m.if the water strikes a wall normally, calculate the force on the wall , assuming the velocity of water normal to the wall is zero after striking?
To calculate the force on the wall, we can use the principle of conservation of momentum.
Step 1: Calculate the mass of the water flowing through the hole.
Given that the area of the hole is 50 cm^2 = 0.005 m^2, and the water is ejected at a speed of 0.3 m/s, we can calculate the flow rate of the water:
Flow rate = Area × Velocity
Flow rate = 0.005 m^2 × 0.3 m/s = 0.0015 m^3/s
The density of water is approximately 1000 kg/m^3, so the mass of the water flowing per second is:
Mass = Flow rate × Density
Mass = 0.0015 m^3/s × 1000 kg/m^3 = 1.5 kg/s
Step 2: Calculate the change in momentum of the water.
The initial momentum of the water is given by:
Initial Momentum = Mass × Initial Velocity
Initial Momentum = 1.5 kg/s × 0.3 m/s = 0.45 kg·m/s
Since the velocity of the water normal to the wall after striking is zero, the final momentum of the water is zero.
Therefore, the change in momentum is:
Change in Momentum = Final Momentum - Initial Momentum
Change in Momentum = 0 - 0.45 kg·m/s = -0.45 kg·m/s
Step 3: Calculate the force on the wall.
The force experienced by an object is equal to the rate of change of momentum. So, we can determine the force on the wall using the following equation:
Force = (Change in Momentum) / (Time taken)
Since the water stops immediately after striking the wall, the time taken is considered to be very small and almost instant.
Therefore,
Force = -0.45 kg·m/s / (very small time)
Since the time is almost instant, the force experienced on the wall will be very large (approaching infinity).
Note: This calculation assumes that there are no other external forces acting on the water or the wall.
To calculate the force on the wall, we need to apply Newton's second law of motion, which states that force (F) is equal to the rate of change of momentum (mass (m) times velocity (v)).
First, we need to convert the area of the hole from square centimeters to square meters. Since 1 m = 100 cm, the area of the hole is 50 cm^2 * (1 m^2 / 10000 cm^2) = 0.005 m^2.
Next, we can calculate the mass flow rate (m_dot) of water using the equation:
m_dot = velocity * area
m_dot = 0.3 m/s * 0.005 m^2
m_dot = 0.0015 kg/s
Since the velocity of water normal (perpendicular) to the wall after striking is zero, the change in momentum is equal to the initial momentum. The initial momentum is given by:
momentum = mass * velocity
momentum = 0.0015 kg/s * 0.3 m/s
momentum = 0.00045 kg*m/s
Therefore, the force exerted on the wall is equal to the change in momentum, which is:
force = momentum / time
However, we need to know the time it takes for the water to strike the wall. Without this information, we cannot calculate the force accurately.
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The force according to the Newton’s 2 Law is
F= m•a=m•(Δv/Δt) =Δ(m•v)/ Δt
If the length of the moving stream is L and the density of water is ρ, then
F = (ρ•S•L•v)/(L/v) = ρ•S•v^2 =
=1000• 50•10^-4•(0.3)^2=0.45 N