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A ball of Mass M is swung in a vertical circle with a constant tangential speed. Figure 1 shows the forces exerted on the ball at the top of the circle, and Figure 2 shows the forces exerted on the ball at the bottom of the circle. Which of the following is an expression for the centripetal acceleration of the ball in terms of M, T1, T2, and any fundamental constants?

A ball of Mass M is swung in a vertical circle with a constant tangential speed Figure 1 shows the forces exerted on the ball at the top of the circle and Figur class=

Respuesta :

JDtheFast

Answer:

T1+T2/2M

Explanation:

onyebuchinnaji

The expression for the centripetal acceleration for the vertical circle is [tex]a_c = \frac{T_1 + T_2 }{2m}[/tex].

In a vertical circular motion, the tension of the swing at the top of the circle is given as;

[tex]T_1 =m a_c_{top} - mg\\\\T_1 = ma_c - mg\\\\mg = ma_c - T_1[/tex]

The tension of the swing at the bottom of the circle is given as;

[tex]T_2 = ma_{bottom} + mg\\\\T_2 = ma_c + mg[/tex]

solve the two equations together;

[tex]T_2 =ma_c + ( ma_c -T_1)\\\\T_2 = ma_c + ma_c - T_1\\\\T_2 + T_1 = 2ma_c\\\\a_c = \frac{T_1 + T_2}{2m}[/tex]

Thus, the expression for the centripetal acceleration for the vertical circle is [tex]a_c = \frac{T_1 + T_2 }{2m}[/tex].

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