A 0.2 kg mass hangs at the end of a wire. what is the tension in the wire if the ball is whirled around in a horizontal circle with tangential velocity of 5 m/sec
Let the tension be T and the angle of the string to the horizontal be A.
Write equations for horizontal and vertical motion.
T sin A = M g
T cos A = M V^2/r
Square both sides and add the two equations to get T
T^2(sin^2A + cos^2A) = T
= M^2(g + V^2/r)
Solve for T.
You need to know the length of the wire (r) to solve this problem. They should have told you what it is.
A person places the speakers 4.0 m apart and connects a signal generator to both speakers that produces a single and consistent tone. (constant wavelength and frequency) He then walks to a point that is 2.0 m from one speaker and 2.3 m from the other. At that point he notices a quiet “spot”. If the speed of the sound in the room is known to be 350 m/s, calculate the possible frequencies being played by the speakers.
My Answer:
PD=2.3m-2m
PD=.3m
PD=(n-.5) λ, but λ=v/f
PD=(n-.5)(v/f)
.3=(n-.5)(350/f)
f=(n-.5)(350/.3)
f=(n-.5)(3500/3)
f=(3500n/3)-(3500/6)
f=(3500n/3)-(3500/6), where n is any real integer.
Is this right? Thanks for your help.
To find the tension in the wire, we need to consider the forces acting on the mass as it moves in a horizontal circle.
In this case, the tension in the wire provides the centripetal force required to keep the mass moving in a circle. The centripetal force is given by the formula:
F = (m * v²) / r
Where:
F is the centripetal force
m is the mass
v is the tangential velocity
r is the radius of the circle
In this problem, the mass is 0.2 kg and the tangential velocity is 5 m/s.
However, the radius of the circle is not provided. So, we need to determine the radius of the circle in order to calculate the tension in the wire.
To find the radius, we can use the formula for the circumference of a circle:
C = 2 * π * r
The tangential velocity, v, is given by:
v = C / T
Where:
C is the circumference of the circle
T is the time taken to complete one revolution
In this case, we can assume that the time taken to complete one revolution is the period of rotation, T. So, the formula can be written as:
v = 2 * π * r / T
Now, rearranging the formula, we can solve for r:
r = v * T / (2 * π)
To calculate the radius of the circle, we need to know the period of rotation, T. If the period is not given, we cannot find the tension in the wire without additional information.