Length of the copper rod = 2.5 meters
Speed at which sound travels through copper = 3560 meter per second
Let us assume the time taken
by sound to cover the given distance = x seconds
We already know that
Speed = Distance/ Time
Then
Time = Distance/ Speed
x = 2.5/3560 seconds
= 0.0007 seconds.
This can ve done by hitting one end of the rod and then receiving the sound at the other end and using the stop clock to measure the time taken.
Answer:
W = (F1 - mg sin θ) L, W = -μ mg cos θ L
Explanation:
Let's use Newton's second law to find the friction force. In these problems the x axis is taken parallel to the plane and the y axis perpendicular to the plane
Y Axis
N - =
N = W_{y}
X axis
F1 - fr - Wₓ = 0
fr = F1 - Wₓ
Let's use trigonometry to find the components of the weight
sin θ = Wₓ / W
cos θ = W_{y} / W
Wₓ = W sin θ
W_{y} = W cos θ
We substitute
fr = F1 - W sin θ
Work is defined by
W = F .dx
W = F dx cos θ
The friction force is parallel to the plane in the negative direction and the displacement is positive along the plane, so the Angle is 180º and the cos θ= -1
W = -fr x
W = (F1 - mg sin θ) L
Another way to calculate is
fr = μ N
fr = μ W cos θ
the work is
W = -μ mg cos θ L
I uploaded the answer to a file hosting. Here's link:
tinyurl.com/wtjfavyw
The important point here is that volumetric flow rate in the pump and the pipe is the same.
Q = AV, where Q = Volumetric flow rate, A = Cross sectional area, V = velocity
Q (pump) = (π*15^2)/4*2 = 353.43 cm^3/s
Q (pipe) = (π*(3/10)^2)/4*V = 0.071V
Q (pump) = Q (pipe)
0.071V = 353.43 => V = 5000 cm/s
Therefore, the flow of water in the pipe is 5000 cm/s.
Answer: vf= 51 m/s and d= 112 m
Explanation: solution attached