JBA said:
Without seeing a clear and complete description the problem(s) and your attempted solution(s) there is no way to evaluate your difficulties.
Introduction
This experiment uses water jets impacting on metal plates to look at Newton’s second law.
Aim
The aim of the experiment is to compare the forces acting on the two metal plates.
Background and Analysis
Newton’s second law of motion states that the force acting on a body is equal to the rate of change of momentum. You may be familiar with the special case , which is only true when the mass is constant.
In this experiment, we have fluid flowing, and so there is not a fixed mass. Newton’s second law, in this case, can be written
where: is the (vertical) force acting on the fluid, is the mass flow rate,
and are the initial and final fluid velocities vectors (positive for upwards, negative for downwards), is a momentum flux.
Suppose the water exits the nozzle with a vertical velocity of , i.e. .
In the case of the flat plate, the water spreads out horizontally; the final vertical velocity is zero, . The force acting on the fluid is . Note the minus sign means that the force acting on the fluid is downwards.
In the case of the hemispherical shell, the water comes off the plate traveling vertically downwards. If we assume that the fluid speed is constant ( ) and only changes direction, then final velocity is ; note the minus sign because the fluid is going downwards. The force acting on the fluid in this case is double that of the flat plate.
Procedure
- Starting with the flat plate, move the jockey weight 2cm along the lever arm.
- Open the control valve and change the flow rate until the lever arm is level.
- Measure the mass flow rate of water by measuring the length of time taken to collect a volume of water.
- Repeat each measurement moving the jockey weight further down the lever arm in 2cm increments.
- Each time note the distance of the jockey weight, the mass of water collected, and the time taken (there is a
table at the back of the lab sheet for you to record your measurements).
- You can repeat each measurement several times to find an average.
- Repeat the test for the hemispherical shell.
Analysis of Results
For each measurement, calculate the mass flow rate dot/t
Where: m dot is the mass flow rate
m is the mass of water collected
t is the time of collection
- If you took multiple measurements, find the average mass flow rate (add them up and divide by the number of values)
- Calculate the force acting downwards due to the jockey weight
Fv = mjgb/a
https://www.physicsforums.com/file:///page2image3816
where:
Fv is the vertical force acting on the fluid
mj = 0.61kg is the mass of the jockey weight,
g = 9.81 m/s^2 is acceleration due to gravity,
a = 152.4 mm is the distance of the neutral position from the pivot,
b is the distance of the jockey weight from the neutral position
I can't insert the image but is that of the setup of the hydraulic bench (jockey and plate part)
Figure 1: The forces acting on the balance beam in equilibrium when (a) there is no force on the plate and (b) the water jet produces a force on the plate and the jokey mass is moved to re-establish equilibrium. Note that in figure a) the torque produced from the spring force, S, cancels the torque from the jockey mass and the pass of the beam.
Presentation of results
On the same graph, plot against for both sets of results Find the line of best fit for each set of results
Discussion
How do the lines of best fit compare with the theory above?
What are the sources of error in the experiment? Could these be reduced or eliminated? Quantify the effect of the errors on your results.
Conclusions
Report your best fit equations and summarise the important points that arose in your discussion. that's the problem I just need to understand why is that the results from the calculation of the average rate of change of momentum for the flat place are double that of the hemispherical plate when the theory says the opposite.
