In a water pistol, a piston drives water through a larger tube of radius 1.00 cm into a smaller tube of radius
1.00 mm.
(a) If the pistol is fired horizontally at a height of 1.5m, use ballistics (2-D projectile motion) to determine the
time it takes water to travel from the nozzle to ground. (Neglect air resistance and assume atmospheric
pressure of 1 atm.)
(b) If the range of the stream is 8.00m, with what speed must the stream leave the nozzle?
(c) Given the areas of the nozzle and the cylinder, use the equation of continuity to calculate the speed with
Which the plunger must be moved.
(d)What is the pressure at the nozzle?
(e)Use Bernoulli’s equation to find the pressure in the larger cylinder. Can gravity terms be neglected?
(f) Calculate the force that must be exerted on the trigger on the trigger to achieve the desired range. (The
Force that must be exerted is due to the pressure above atmospheric pressure.)
ive been sick so i missed a few classes and im not sure whats going on in my class these are my homework problems im trying to keep up
To solve each of the questions, we'll need to use various equations and principles from physics. Let's break down each question and explain how to find the answers:
(a) To determine the time it takes for the water to travel from the nozzle to the ground, we'll use projectile motion equations. Since we are neglecting air resistance and assuming atmospheric pressure, the motion of the water can be treated as a 2-dimensional projectile. We need to find the time it takes for the water to reach a height of 1.5m.
- Start by finding the initial velocity of the stream at the nozzle. This can be calculated using the equation: v0 = sqrt(2gh), where g is the acceleration due to gravity (9.8 m/s^2) and h is the height (1.5m).
- Once you have the initial velocity, v0, you can use the equation: h = v0*t - (1/2)gt^2 to solve for the time, t.
(b) To find the speed with which the stream must leave the nozzle in order to have a range of 8.00m, we can use the range equation for projectile motion.
- The range, R, can be calculated using the equation: R = v0x * t, where v0x is the horizontal component of the initial velocity.
- Rearrange the equation to solve for v0x: v0x = R / t.
- Substitute the given values of R and the time obtained in part (a) to find v0x.
(c) Using the equation of continuity, we can calculate the speed at which the plunger must be moved to maintain a constant flow rate. The equation of continuity states that the product of the cross-sectional area and the speed of flow must be constant along a streamline.
- The cross-sectional area of the nozzle and the cylinder can be used to calculate the speed, v, using the equation: A1v1 = A2v2, where A1 and A2 are the areas, and v1 and v2 are the speeds at those areas.
- Given the radii of the tubes, you can calculate their respective areas using the formula: A = πr^2.
- Rearrange the equation to solve for v1, and substitute the given values to find v1.
(d) To determine the pressure at the nozzle, we can use Bernoulli's equation, which relates the pressure, velocity, and height of a fluid.
- Bernoulli's equation is given by: P + (1/2)ρv^2 + ρgh = constant, where P is the pressure, ρ is the density of water, v is the velocity of the water, and h is the height.
- Rearrange the equation to solve for P, and substitute the given values to find the pressure at the nozzle.
(e) Using Bernoulli's equation, we can also find the pressure in the larger cylinder. The gravity terms cannot be neglected as it plays a role in determining the pressure difference.
(f) To calculate the force that must be exerted on the trigger to achieve the desired range, we need to consider the pressure difference between the inside and outside of the water pistol.
- The force, F, can be calculated using the equation: F = A * (P - Patm), where A is the area of the nozzle, P is the pressure at the nozzle, and Patm is the atmospheric pressure.
- Substitute the given values to find the force needed to achieve the desired range.
By following these steps and using the appropriate equations, you should be able to find the answers to each of the questions.
anon ~
Wow! 10 posts in 8 minutes!! You must be taking a test.
If you repost these WITH YOUR ATTEMPTS AT SOLUTIONS INCLUDED, they won't be removed.