Based on the tug of war pictured below, what is the net force? –190 N 10 N –10 N 190 N.
1 answer:
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Answer:
The angle θ is 6.1° below the horizontal.
Explanation:
Please, see the figure for a description of the situation.
The vector "r" gives the position of the ball and can be expressed as the sum of the vectors rx + ry (see figure).
We know the magnitude of these vectors:
magnitude rx = 11.6 m
magnitude ry = 2.23 m - 0.99 m = 1.24 m
Then:
rx = (11. 6 m, 0)
ry = (0, -1.24 m)
r = (11.6 m + 0 m, 0 m - 1.24 m) = (11.6 m, -1.24 m)
Using trigonometry of right triangles:
magnitude rx = r * cos θ = 11. 6 m
magnitude ry = r * sin θ = 2.23 m - 0.99 = 1.24 m
where r is the magnitude of the vector r
magnitude of vector r:
Then:
cos θ = 11.6 m / 11.667 m
θ = 6.1°
Using ry, we should obtain the same value of θ:
sin θ = 1.24 m/ 11.667 m
θ = 6.1°
( the exact value is obtained if we do not round the module of r)
