Question

a 5kg bucket hangs from a ceiling on a rope. A student attaches a spring scale to the buckets handle and pulls horizontally on the scale until reads 15.0 N.

a. draw a force diagram that will be useful in answering the questions below

b. calculate the tension in the rope attached in the rope attached to the ceiling when the spring scale reads 15N.

c. Determine the measure of the angle marked in the diagram

have the force diagram but cannot figure out the angle or how to calculate the tension.

Answer 1

I don’t know what the angle is in your diagram so I used the angle from the vertical.

Answer 2

Tension is a force that works in the string or rope under an applied force. The resulting tension on the given rope is 51.24 N at the angle of 17°.

Tension calculated by:

Calculating the horizontal and verticle forces:

The total horizontal force,

$\Sigma F_x = 15\rm \ N - \it T\rm sin \Theta$

Total vertical force,

$\Sigma F_y = \it T\rm cos\Theta - 49 \rm\ N$

The total tension,

$T = \sqrt {15 ^2 +49^2}\\\\ T = 51 .24 \rm \ N$

The angle of resulting tension,

$\Theta = \rm sin ^{-1} \dfrac {15 }{51.24}\\\\ \Theta = 17 ^o$

Therefore, the resulting tension on the given rope is 51.24 N at the angle of 17°.

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