EARN MORE EMARKS The other solution, d- -0.437 m, can be rejected because d was

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EARN MORE EMARKS The other solution, d- -0.437 m, can be rejected because d was chosen to be a positive umber at the outset. A change in the acrobat's center of mass, say, by crouching as she makes contact ith the springboard, also affects the spring's compression, but that effect was neglected. Shock absorbers often Involve springs, and this example Illustrates how they work. The spring action of a shock absorber turns a dangerous jolt Into a smooth deceleration, as excess kinetic energy is converted to spring potential energy QUESTION Is it possible for the acrobat to rebound to a height greater than her initial height? Explain No. The kinetic energy that the acrobat gains on the way down is converted entirely back into Yes. The acrobat can bend her knees while falling and then straighten them as if jumping when O Yes. Elastic energy is always present in the spring and can give the acrobat greater height than Yes. The acrobat can provide mechanical energy by pushing herself up while in contact with the (Select all that apply.) potential energy when she reaches the initial height. bouncing upward again. initially springboard. O No. There is no external source of energy to provide the potential energy at a greater height. PRACTICE IT Use the worked example above to help you solve this problem. A 54.2 kg circus acrobat drops from a height of 1.84 meters straight down onto a springboard with a force constant of 8.16 x 103 N/m, as shown in the figure. By what maximum distance does she compress the spring? EXERCISE HINTS: GETTING STARTED I M STUCK! An 7.75 kg block drops straight down from a height of 0.93 m, striking a platform spring having a force constant of 1.12 × 103 N/m. Find the maximum compression of the spring. Need Help? Talk to s Tutor

Explanation / Answer

1.

2.Yes acrobat can bend her knees while falling and then straighten them as if jumping when bouncing upward again

4.yes the acrobat can provide mechanical energy by pushing herself up while in contact with the spring board

2.

By Conservation of energy

mgh =(1/2)Kd2+mg(-d)

mg(h+d)=(1/2)*K*d2

54.2*9.81*(1.84+d)=(1/2)*8160*d2

4080d2-531.7-978.3=0

d=0.559 m =0.56 m(approx)

3.

By Conservation of energy

mg(h+d)=(1/2)Kd2

7.75*9.81*(0.93+d)=(1/2)*1120*d2

560d2-76.03-70.7=0

d=0.4296 m =0.43 m

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