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A child of mass 28 kg swings at the end of an elastic cord. At the bottom of the swing, the child's velocity is horizontal, and the speed is 7 m/s. At this instant the cord is 3.30 m long. (Take the +x direction to be horizontal and to the right, the +y direction upward and +z direction to be out of the page.)

a. At this instant, what is the magnitude of the rate of change of the child's momentum?
b. At this instant, what is the (vector) net force acting on the child?

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Answer:

Explanation:

(A)

Force is said to be the rate of change of momentum.

At the instant, the parallel component of the change of momentum is zero. SInce centripetal force always acts towards the center, hence the direction upwards ( along the positive y-axis).

[tex]\dfrac{dp}{dt} = F(+\hat y)[/tex]

[tex]= \dfrac{mv^2}{r}(+\hat y) \ \\ \\ = \dfrac{28 \ kg \times (7 \ m/s)^2}{3.3 \ m }( + \hat y) \\ \\ = \mathbf{416 \ N ( + \hat y)}[/tex]

(B)

The net force acting on the child is:

[tex]F_{net} = \dfrac{mv^2}{r}( + \hat y) \\ \\[/tex]

[tex]= \dfrac{28 \ kg \times (7 \ m/s)^2}{3.3 \ m }( + \hat y) \\ \\ = \mathbf{416 \ N ( + \hat y)}[/tex]

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