A simple pendulum consists of a ball of mass
5.39 kg hanging from a uniform string of mass
0.0789 g and length L. The period of oscilla-
tion for the pendulum is 2.51 s.
Determine the speed of a transverse wave
in the string when the pendulum is station-
ary and hangs vertically. The acceleration of gravity is 9.8 m/s2 .
Answer in units of m/s.
post your work, please, I will check it. Ahhh. did you work mass in kg?
i have sample homework with solution and different numbers. Mass=5.51kg Ms=0.0754g T=1.39s.
g(1.39)^2/4*pi^2=.4796
sqrt(5.51/(.000754/.4796))=59.2
answer on this problem is 586.072 m/s
To find the speed of a transverse wave in the string when the pendulum is stationary and hangs vertically, we can use the formula:
v = √(T/μ)
Where:
- v is the speed of the transverse wave in the string
- T is the tension in the string
- μ is the linear mass density of the string
To find T, we can use the weight of the ball as the tension in the string when the pendulum is stationary and hangs vertically.
T = mg
Where:
- m is the mass of the ball
- g is the acceleration due to gravity
To find μ, we need to calculate the linear mass density of the string.
μ = mₛ / L
Where:
- mₛ is the mass of the string
- L is the length of the string
Given:
- Mass of the ball, m = 5.39 kg
- Mass of the string, mₛ = 0.0789 g = 0.0000789 kg
- Length of the string, L (not provided)
- Period of oscillation, T = 2.51 s
- Acceleration due to gravity, g = 9.8 m/s²
To find L, we will use the formula for the period of a pendulum:
T = 2π √ (L / g)
Rearranging the equation to solve for L:
L = (T² g) / (4π²)
Substituting the given values:
L = (2.51² * 9.8) / (4π²)
Once we have L, we can calculate μ using the mass of the string:
μ = mₛ / L
Finally, we can calculate v using the formula:
v = √(T/μ)
Just substitute the values of T and μ that we calculated.
This will give us the speed of the transverse wave in the string when the pendulum is stationary and hangs vertically.
Ignore the mass of the string in determining the period of the pendulum.
Tension=5.39g
massperunitlengthstring=.0789/L
periodpendulum=2PI sqrt (L/g)
solve for L, given pendulum.
wavespeed= (from the law of string)
wavespeed= sqrt (Tension/(mass/length))