Respuesta :
Answer:
Centripetal force, [tex]F_x=0.379\ N[/tex]
Explanation:
It is given that,
Mass of the ball, m = 62 g = 0.062 kg
Length of the string, l = 72 cm = 0.72 m
Angle, [tex]\theta=32^{\circ}[/tex]
To find,
The centripetal force experienced by the ball.
Solution,
According to the attached free body diagram,
[tex]T\ cos\theta-mg=0[/tex]
[tex]T=\dfrac{mg}{cos\theta}[/tex]
[tex]T=\dfrac{0.062\times 9.8}{cos(32)}[/tex]
T = 0.716 N
The centripetal force will be experienced by the ball in horizontal direction. It is equal to :
[tex]F_x=T\ sin\theta[/tex]
[tex]F_x=0.716\ N\ sin(32)[/tex]
[tex]F_x=0.379\ N[/tex]
So, the centripetal force experienced by the ball is 0.379 N.
The centripetal force experienced by the small ball if mass 62 g and attached to the string is 0.379 N.
What is centripetal force?
Centripetal force is the force which is required to keep rotate a body in a circular path. The direction of the centripetal force is inward of the circle towards the center of rotational path.
Given information-
The mass of the small bag is 62 grams.
The length of the string is 72 cm.
Suppose T is the tension in the string, m is the mass of ball and g is the gravitational force.
The horizontal force applied on the body is,
[tex]\sum F_x=T\cos \theta-mg=0\\T=\dfrac{mg}{\cos \theta}[/tex]
The centripetal force applied on the body is,
[tex]F_c=T\sin \theta\\T=\dfrac{F_c}{\sin \theta}[/tex]
Compare both the values of the T, we get,
[tex]\dfrac{F_c}{\sin\theta}=\dfrac{mg}{\cos \theta}\\{F_c}=\dfrac{mg\times{\sin\theta}}{\cos \theta}\\{F_c}={mg\times{\tan\theta}}[/tex]
Put the values as,
[tex]F_c=0.062\times9.8\times\tan(32)\\F_c=0.379\rm N[/tex]
Thus, the centripetal force experienced by the small ball if mass 62 g and attached to the string is 0.379 N.
Learn more about the centripetal force here;
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