Net Muzzle
physics homework?
2. A(n) 8 g bullet leaves the muzzle of a rifle
with a speed of 419.5 m/s.
What constant force is exerted on the bullet
while it is traveling down the 0.6 m length of
the barrel of the rifle? Answer in units of N.
3.A 1501.6 kg car is traveling at 25.8 m/s when
the driver takes his foot off the gas pedal. It
takes 4.7 s for the car to slow down to 20 m/s.
How large is the net force slowing the car?
Answer in units of N.
4.A person of mass 79.6 kg escapes from a burn-
ing building by jumping from a window situ-
ated 27.7 m above a catching net.
The acceleration of gravity is 9.8 m/s2 :
If air resistance exerts a force of 93 N on
him as he falls, determine his speed just before
he hits the net. Answer in units of m/s.
The equations you will need to use to solve these problems are:
Equation 1: Force (N) = mass (kg) * acceleration (m/s^2);
Equation 2: X(f) = X(i) + V(i) + 0.5 * acceleration * time^2;
Equation 3: V(f) = V(i) + acceleration * time;
(f) = final, (i) = initial, X = position (m), V = Velocity (m/s).
For #2, you know final postion (0.6 m) and final velocity (419.5 m/s). You also know that initial position and initial velocity are both equal to zero. But you do not know either acceleration (a) or time. So since you have two unknowns you must use both equation 2 and equation 3 and solve both equations for time. This will give you:
square root (2 * X(f) / a) = time = V(f) / a or;
square root (2 * X(f) / a) = V(f) / a
Solving for a gives:
a = V(f) / [2 * X(f)] = (419.5 m/s)^2 / [2 * .6 m]
a = 146650 m/s^2
You can verify the answer is correct by solving equation 3 for time and using that answer for time to solve equation 2 for final position which is already known.
Now that you know acceleration you use equation 1 to find the force exerted on the bullet. You need to remember that a Newton = kilogram * meter / sec^2 and the mass of the bullet is given in grams. Solving gives:
F(N) = 0.008 kg * 146650 m/s^2 = 1173 N which is the answer to # 2.
For # 3 you know V(f), V(i), and time. So the only unknown in equation 3 is the acceleration. So solving equation 3 for acceleration gives:
a = [V(f) - V(i)] / time = [20 m/s - 25.8 m/s] / 4.7 sec = -1.234 m/s^2
Now that you know acceleration and mass you can solve for force: Using equation 1 gives:
F(N) = 1501.6 kg * -1.234 m/s^2 = -1853 N
Note that the problem asks for the size of the force and not the direction of the force. So your answer should be the absolute value of the force = 1853 N and is the answer for # 3.
For question # 4, you first need to solve for the downward force due to gravity. Using equation 1 this gives:
F(N) = 79.6 kg * 9.8 m/s^2 = 780 N
Now you are given an opposing force to gravity that is equal to 93 N. Assume that the positive direction is down this and summing the forces gives:
F(total N) = 780 N - 93 N = 687 N
Solving the total forces for the acceleration rate using equation 1 gives:
a (m/s^2) = F(total N) / mass (kg) = 8.63 m/s^2
Now that you know the rate of acceleration you use equation 2 to solve for the time it takes the person to reach the net. To make the calculations simple you set the window the person jumps from as the zero position in your problem. This gives both X(i) and V(i) = 0. Solving equation 1 for time gives:
t (sec) = square root [ (2 * X(f) / a] =
square root [ (2 * 27.7 m) / 8.63 m/s^2] = 2.53 sec
To find the speed of the person just as he contacts the net use equation 3 and solve for V(f):
V(f) = V(i) + (a * t) = 0 + 8.63 m/^s^2 * 2.53 sec = 21.87 m/s which is the answer to part 4.
I hope this helps and you need to study through the process so you know how to do these problems on an exam. Also be sure to carry units through as you work the problem. This will help to assure that you get a correct answer to the problem.
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How does a net relief muzzle net work and what is it for? How do you put it on?
I never used one, and never heard of it until you asked, so I found some. It attaches to the bridle noseband, and is a fine net that covers over the muzzle area. It is supposed to stop head shaking in 79% of cases, since most are caused by midges and other flying insects. Other cases are related to pollen, and I doubt the net can completely prevent pollen from being breathed. Anyway, I hope someone answers who has actually used one. The sites I saw said they are allowed in at least some showrings.
