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A heavy steel ball is hung from a cord to make a pendulum. The ball is pulled to the side so that the cord makes a 5 ∘ angle with the vertical. Holding the ball in place takes a force of 40 N . If the ball is pulled farther to the side so that the cord makes a 10 ∘ angle, what force is required to hold the ball?

Respuesta :

Answer:

The required force is calculated as 79.69 N

Solution:

As per the question:

Angle, [tex]\theta = 5^{\circ}[/tex]

Force, F = 40 N

The angle after the ball is being pulled, [tex]\theta' = 10^{\circ}[/tex]

Now,

To calculate the required force:

The tension in the string can be calculated by considering the vertical component:

[tex]F = Tsin\theta[/tex]

where

T = Tension in the cord

Now,

[tex]T = \frac{F}{sin\theta} = \frac{40}{sin5^{\circ}} = 458.94\ N[/tex]

Now, after the cord is being pulled, the force exerted is given by:

[tex]F' = Tsin\theta' = 458.94\times sin10^{\circ} = 79.69\ N[/tex]

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