A string with a mass of 0.034 kg has a length of 4.80 m. If the tension in the string is 100.00 N and a sinusoidal wave with an
amplitude of 2.40 cm is induced on the string, what must the frequency (in Hz) be for an average power of 200.00 W
1 answer:
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Answer:
9.4 m/s
Explanation:
According to the work-energy theorem, the work done by external forces on a system is equal to the change in kinetic energy of the system.
Therefore we can write:
where in this case:
W = -36,733 J is the work done by the parachute (negative because it is opposite to the motion)
is the initial kinetic energy of the car
is the final kinetic energy
Solving,
The final kinetic energy of the car can be written as
where
m = 661 kg is its mass
v is its final speed
Solving for v,
Answer:
a. Fab = 3000 N tension
Fac = 1500 N compression
Fbc = 3000 N compression
b. Aluminum for AB, titanium for AC and BC.
c. Fc = 4000 N
Explanation:
a. Draw free body diagrams of the pins at A and B, assuming that all internal forces are in tension (pulling away from the pin).
Sum of the forces on A in the x direction:
∑F = ma
H − Fab sin 60° = 0
Fab = H / sin 60°
Fab = 2600 / sin 60°
Fab = 3000 N
Sum of the forces on A in the y direction:
∑F = ma
-Fab cos 60° − Fac = 0
Fac = -Fab cos 60°
Fac = -H / tan 60°
Fac = -2600 / tan 60°
Fac = -1500 N (it's negative, so it's actually in compression).
Sum of the forces on B in the x direction:
∑F = ma
Fab cos 30° + Fbc cos 30° = 0
Fbc = -Fab
Fbc = -H / sin 60°
Fbc = -3000 N (it's negative, so it's in compression)
b. AB is in tension, so it should be aluminum.
AC and BC are in compression, so they should be titanium.
c. Draw a free body diagram of the entire triangle ABC. Assume there is both a horizontal and vertical reaction force at C, and assume they point in the +x and +y directions.
Sum of the forces in the x direction:
∑F = ma
Fcx + H = 0
Fcx = -H
Fcx = -2600 N
Sum of the forces in the y direction:
∑F = ma
Fcy − V = 0
Fcy = V
Fcy = 3000 N
The magnitude of the net force is:
Fc² = Fcx² + Fcy²
Fc² = (-2600 N)² + (3000 N)²
Fc = 4000 N
