Similar to the situation shown in figure (a) below, a toy plane is being whirled

Question

Similar to the situation shown in figure (a) below, a toy plane is being whirled at constant speed in a horizontal circle. The plane is attached to a string of length L. Figure (b) shows the relevant free-body diagram; figure (c) shows the coordinate system; and figure (d) shows the free-body diagram with the force of tension split into components.

(a) Use g = 10 m/s2, a speed for the plane of 1.70 m/s, and the angle = 32.0 degrees. Determine the length of the string.

m

(b) The mass of the plane is 0.211 kg. Calculate the tension in the string.

2.47

N

(c) It may be a little surprising to you to note that the magnitude of the tension in the string is actually larger than the magnitude of the force of gravity acting on the plane. In which other situations is this also true? (Select all that apply.)

Explanation / Answer

a) Digram is missing,

so i assume that angle 32 degree is given is angle of string with vertical.

if it is with horizontal then change all 32 with (90 -32 = 58 ) .

in horizontal,

Tsin32 = mv^2 / R

in vertical,
Tcos32 = mg

Tsin32/Tcos32 = tan32 = v^2 / Rg

R = 0.462 m

sin32 = R /L

L = 0.462/sin32 = 0.873 m

b) T = mg / cos32 = (0.211x 9.81 / cos32) = 2.44 N

c) situtation are not given

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