Answer:
The length of the pipe A is = 0.4763 m & the length of the pipe B is
0.357 m
Explanation:
Fundamental frequency = 360 Hz
Velocity = 343
(a). Length of the pipe is given by
Put all the values in above equation we get
= 0.4763 m
(b). Given that
The third harmonic of organ pipe B = the second harmonic of pipe A
Thus
Put all the values in above formula we get
0.357 m
Therefore the length of the pipe A is = 0.4763 m & the length of the pipe B is
0.357 m
(a) -4.6 m/s
We can solve this part by using the law of conservation of momentum: in fact, the total momentum of the bullet-rifle system before and after the shot must be equal.
Before the shot, the total momentum is zero:
p = 0 (1)
After the shot, the total momentum is:
(2)
where
m = 0.0250 kg is the mass of the bullet
v = 550 m/s is the velocity of the bullet
M = 3.00 kg is the mass of the rifle
V is the recoil velocity of the rifle
Since momentum is conserved, (1) = (2), so we can solve for V:
And the negative sign means the rifle will move backward.
(b) 31.7 J
The kinetic energy of an object is given by
where
m is the mass of the object
v is its speed
The rifle has a mass of
M = 3.00 kg
And a final speed of (speed = magnitude of velocity)
V = 4.6 m/s
Therefore, the kinetic energy it has gained is
(c) -0.5 m/s
In this case, we just need to repeat the problem as in part (a), applying the law of conservation of momentum:
where in this case, the mass of the rifle is
M = 28.0 kg
while the other data are unchanged:
m = 0.0250 kg is the mass of the bullet
v = 550 m/s is the velocity of the bullet
Solving for V, we find the new recoil velocity of the rifle:
(d) 3.5 J
As in part b), we can apply the equation of the kinetic energy:
The kinetic energy of an object is given by
where in this case, we have:
M = 28.0 kg is the mass of the rifle+shoulder
V = 0.5 m/s is the recoil speed of the rifle+shoulder
Substituting into the equation,
(e) Player's momentum is larger
The momentum of the player is
where
M = 110 kg is the mass of the player
V = 8.00 m/s is his velocity
Substituting,
The momentum of the ball is
where
m = 0.410 kg is the mass of the ball
v = 25.0 m/s is the velocity of the ball
Substituting,
The player's momentum is much larger than the ball's momentum. This problem becomes similar to the previous one in the moment when the player catches the ball: at that point, in fact, the velocity of the player-ball system will change such that their total combined momentum will be equal to the total momentum of the two individual objects before the catch.