Question

8. A 60-ks gymnast is moving with a speed of 12.0 m/s when she lands on the ground during an

event. If she bends her knees upon contact with the ground, then she will increase the time of
collision by a factor of 20 - compared to if she keeps her knees stiff. What affect does this have
upon the force and the impulse that she experiences? Mark all that apply
a. Bending her knees will make the force 20 times greater.
b. Bending her knees will make the force 20 times smaller.
c. Bending her knees will make the impulse 20 times greater.
d. Bending her knees will make the impulse 20 times smaller.
e. Bending her knees will have no effect upon the impulse she experiences.

Answer 1

B. Bending her knees will make the force 20 times smaller.

Step-by-step explanation:

By the Impulse Theorem, we notice that the normal force from the ground to the gymnast counteract the intial linear momentum of the gymnast during a certain time until rest is reached. The impulse (
`Imp`), measured in newton-second, is function of initial linear momentum, measured in kilogram-meters per second, only and, hence, remains constant. That is:

`Imp = m\cdot v` (1)

Where:

`m` - Mass of the gymnast, measured in kilograms.

`v` - Initial speed of the gymnast, measured in meters per second.

If we know that
`m = 60\,kg` and
`v = 20\,(m)/(s)`, the impulse experimented by the gymnast is:

`Imp = (60\,kg)\cdot\left(12\,(m)/(s) \right)`

`Imp = 720\,(kg\cdot m)/(s)`

If the time of collision is increased by a factor of 20 by bending her knees, then normal force from the ground on the gymnast must be decrased by a factor of 20 in order to keep the impulse constant.

Therefore, the right answer is B.