A child of mass 27 kg swings at the end of an elastic cord. At the bottom of the

Question

A child of mass 27 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 11 m/s. At this instant the cord is 4.90 m long. (Take the +x direction to be horizontal and to the right, the +y direction to be upward, and the +z direction to be out of the page.)

(a) At this instant, what is the parallel component of the rate of change of the child's momentum?

The answer of this is 0

(b) At this instant, what is the perpendicular component of the rate of change of the child's momentum?

666.7 is not correct

(c) At this instant, what is the net force acting on the child?

Not <0, 402,0>

(d) What is the magnitude of the force that the elastic cord exerts on the child? (It helps to draw a diagram of the forces.)

(e) The relaxed length of the elastic cord is 4.82 m. What is the stiffness of the cord? (Use the exact value you entered in part (d) to make this calculation.)

Explanation / Answer

At this instant, there will be no vertical movement. The momentum is not changing. The net force on the child is equal to (mv^2)/r, which is about 340.4. The magnitude of the force the cord exerts on the child is m(v^2/r + 9.8), which is about 585.4.

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