Question

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

Answer 1

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.

Answer 2

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.