A large kite of mass 6.9 kg is flying through the air on a windy day. Currently,
ID: 2166789 • Letter: A
Question
A large kite of mass 6.9 kg is flying through the air on a windy day. Currently, the tension from the string on the kite has a magnitude of 16.5 N at an angle of ? = 34.7 degrees, as indicated in the figure below.
The current acceleration of the kite has a magnitude of a = 7.37 m/s2 at an angle of =397 degrees. The only forces felt by the kite are its own weight, the tension from the string, and a force from the wind. For all questions, use the coordinate system indicated in the figure. Find the x and y component of the force from the wind on the kite.
Stuck on this problem, any ideas? Thanks!
Explanation / Answer
The total force on the kite is m*a, the forces being gravitational pull, the force of the wind, and the force from the string.
The gravitational pull is straight downward with magnitude of mg, or6.9 kg (big kite!) * 9.8 m/sec². The components for this force will therefore be
mx = 0
my = 6.9 * (-9.8) = 67.62 N
The magnitude and direction of the force exerted by the string is known, from which the components can be calculated. The signs and proper trigonometric functions can be determined from the general direction of the vector as illustrated in the diagram and from the reference from which zero angle is measured:
sx = 16.5 N * sin
= 16.5 * sin 34.7°
= 8.55 N
sy = -16.5 N * cos
= -16.5 * cos 34.7°
= -14.1 N
The components of the total force can be calculated as well, by multiplying the acceleration by the mass, giving
fx = m*ax
= 6.9 kg * 7.37 m/sec² * -cos
= 6.9 kg * 7.37 m/sec² * -cos 39.7°
= -41.28 N
fy = m*ay
= 6.9 kg * 7.37 m/sec² * sin
= 6.9 kg * 7.37 m/sec² * sin 39.7°
= 29.6 N
The total force is the sum of its individual parts, in this case, the wind, gravity, and the pull of the string. The only thing we don't know yet are the components of the wind force, which can be gotten by subtracting the gravity and string pull from the wind force. Therefore,
wx = fx - mx - sx
= -41.28 N - 0 - 8.55 N
= -49.83 N
wy = fy - my - sy
= 29.6 N - (-67.62) N - (-14.1) N
= 111.32 N
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