The other solution, d = -0.437 m, can be rejected because d was chosen to be a p

Question

The other solution, d = -0.437 m, can be rejected because d was chosen to be a positive number at the outset. A change in the acrobat's center of mass, say, by crouching as she makes contact with 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. Is it possible for the acrobat to rebound to a height greater than her initial height? Explain. (Select all that apply.) Yes. Elastic energy is always present in the spring and can give the acrobat greater height than initially. No. The kinetic energy that the acrobat gains on the way down is converted entirely back into potential energy when she reaches the initial height. No. There is no external source of energy to provide the potential energy at a greater height. Yes. The acrobat can provide mechanical energy by pushing herself up while in contact with the springboard. Yes. The acrobat can bend her knees while falling and then straighten them as if jumping when bouncing upward again. Use the worked example above to help you solve this problem. A 47.0 kg circus acrobat drops from a height of 2.01 meters straight down onto a springboard with a force constant of 7.94 x 10^3 N/m, as shown in the figure. By what maximum distance does she compress the spring? An 6.57 kg block drops straight down from a height of 1.31 m, striking a platform spring having a force constant of 1.10 x 10^3 N/M. Find the maximum compression of the spring.

Explanation / Answer

Practice : m =47 kg , h =2.01 m , k =7.94*10^3 n/M

From conservation of energy

mgh = (1/2)kx^2

x = [2.mgh/k]^1/2

x = ((2*47*9.8*2.01)/(7940))^0.5

x=0.48 m

Excercise:

m =6.57, h =1.31m , k =1.1*10^3 N/m

From conservation of energy

mgh = (1/2)kx^2

x = [2.mgh/k]^1/2

x = ((2*6.57*9.8*1.31)/(1100))^0.5

x=0.40 m

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