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9966 [12]
3 years ago
7

A 331 N stoplight is hanging in equilibrium from cables as shown. The tension in the right cable is 550 N, and it makes an angle

of 12 degrees with the horizontal. What is the force of tension exerted by the cable on the left side? 114 N 217 N 538 N 580 N
Physics
1 answer:
VARVARA [1.3K]3 years ago
8 0
Let
F=tension of cable on the left
x=angle of left cable makes with the horizontal

Resolve forces vertically (y-direction)
331=550sin(12)+Fsin(x) =>
Fsin(x)=331-550sin(12)=216.649..........(1)

Resolve forces horizontally (x-direction)
Fcos(x)=550cos(12) =>
Fcos(x)=537.981............................(2)

Divide (1) by (2)
tan(x)=Fsin(x)/Fcos(x)=0.40271
x=atan(0.40271) = 21.935 °

From (2),
F=537.981/cos(x)=537.981/0.92761 = 579.965 N

Check:
Fsin(x)+550sin(12)=579.965*sin(21.935)+550*sin(12) = 331.000  ok
Fcos(x)=537.981
550sin(12)=537.981   ok

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A playground slide is inclined 40°. If a boy with a mass of 32 kg slides down for -3meters. How much work is done by gravity on
telo118 [61]

Answer:

the work done by gravity on the boy is 604.62 J

Explanation:

Given;

distance the boy slides, d = 3 m

angle of inclination of the playground, θ = 40⁰

mass of the boy, m = 32 kg

The vertical height, h, above the ground through which the boy falls represents the height of the triangle which is the opposite side.

The distance through which the boy slides, d, represents the hypotenuse side of the right triangle.

sin \theta = \frac{opposite }{hypotenuse} \\\\sin \theta = \frac{h}{d} \\\\h = dsin\theta\\\\h = 3 \times sin(40^0)\\\\h = 1.928 \ m

The work done by gravity on the boy is calculated as;

W = P.E = mgh

             = 32kg x 9.8m/s² x 1.928m

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Therefore, the work done by gravity on the boy is 604.62 J

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