MJC8719
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A 75 kg trampoline artist jumps vertically upward from the top of a platform with a speed of 4.0 m/s. the tampoline is three meters below the platform.
(b) If the trampoline behaves like a spring of spring constant 5.2 104 N/m, how far does he depress it?
when he depressed the trampoline he also moved further downward. So the total change in height is H + x where H = 3.0 meters and x is the distance the trampoline is depressed, not just 3 meters
You can equate energy at the top, when he is motionless, with energy at the bottom, when he is also motionless.
So equating energy...
m g (H + x) = (1/2) k x2
You'll have a quadratic in x. Go ahead and plug in numbers:
75 * 9.8 * ( 3 + x ) = (1/2) * 52000 x2
2205 + 735 x = 26000 x2 ugly. you can div everything by 1000
26 x2 - 0.735 x - 2.205 = 0 and use quadratic eqn
x = ( 0.735 +/- (0.7352 - 4* 26* (-2.205) )1/2 ) / 2*26
x = ( 0.735 +/- 15.16 ) / 52 = -0.277, 0.306
The negative is not valid, so the answer must be 0.306 meters
(b) If the trampoline behaves like a spring of spring constant 5.2 104 N/m, how far does he depress it?
when he depressed the trampoline he also moved further downward. So the total change in height is H + x where H = 3.0 meters and x is the distance the trampoline is depressed, not just 3 meters
You can equate energy at the top, when he is motionless, with energy at the bottom, when he is also motionless.
So equating energy...
m g (H + x) = (1/2) k x2
You'll have a quadratic in x. Go ahead and plug in numbers:
75 * 9.8 * ( 3 + x ) = (1/2) * 52000 x2
2205 + 735 x = 26000 x2 ugly. you can div everything by 1000
26 x2 - 0.735 x - 2.205 = 0 and use quadratic eqn
x = ( 0.735 +/- (0.7352 - 4* 26* (-2.205) )1/2 ) / 2*26
x = ( 0.735 +/- 15.16 ) / 52 = -0.277, 0.306
The negative is not valid, so the answer must be 0.306 meters