Find the weight of a pumpkin hanging from two scales, if scale one reads 55 N, scale two reads 58 N, and the angle θ between the strings coming from the two scales is 121 degrees.

The weight of the pumpkin hanging from the two scales is 98.36 N.

The given parameters;

The weight of the pumpkin hanging from the two scales is equal to the resultant of the two scale readings.

The resultant of the two force is calculated as follows;

R² = a² + b² - 2abcos(θ)

R² = 55² + 58²  - 2(55)(58)cos(121)

R² = 9674.7

Thus, the weight of the pumpkin hanging from the two scales is 98.36 N.

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The weight of the pumpkin is 46.793 newtons.

Explanation:

We consider the string-pumpkin system as our system, in which weight of pumpkin create two distinct tensions through cords. The equations of equilibrium are now described:

(Eq. 1)

(Eq. 2)

Where:

, - Tension through cords, measured in Newtons.

- Weight of the pumpkin, measured in Newtons.

, - Inclination of each cord with respect to the vertical, measured in sexagesimal degrees.

If we know that , , and , the system of equations becomes:

(Eq. 1b)

(Eq. 2b)

From Trigonometry, we remember the following identity:

(Eq. 3)

By applying (Eq. 3) in (Eq. 1b), we get the following expression after expanding and simplifying algebraically:

And we solve the equation for :

Then, the weight of the pumpkin is: ()

The weight of the pumpkin is 46.793 newtons.

energy stored in the capacitor= 9.72 x 10⁻⁴ j

explanation:

the energy stored in the capacitor is given by

e= 1/2 c v²

e= energy stored

c= capacitance= 1.5 µc= 1.5 x 10⁻⁶f

v= potential difference=36 v

so energy stored= e= 1/2 (1.5 x 10⁻⁶) (36)²

energy stored= 9.72 x 10⁻⁴j