I had asked this in homework help recently, but I think I'll ask it here too.
A person reaches a maximum height of 64 cm when jumping straight up from a crouched position. During the jump itself, the person's body from the knees up rises a distance of around 41 cm. To keep the calculations simple and yet get a reasonable result, assume that the entire body rises this much during the jump.
Part A: With what initial speed does the person leave the ground to reach a height of 64 cm?
Part B: In terms of this jumper's weight W , what force does the ground exert on him or her during the jump?
I figured out the first part, but I can't figure out the second part. :(
Also,
It has to be a number? This is online homework and the answer is in the format:
F=_____W
A person reaches a maximum height of 64 cm when jumping straight up from a crouched position. During the jump itself, the person's body from the knees up rises a distance of around 41 cm. To keep the calculations simple and yet get a reasonable result, assume that the entire body rises this much during the jump.
Part A: With what initial speed does the person leave the ground to reach a height of 64 cm?
Part B: In terms of this jumper's weight W , what force does the ground exert on him or her during the jump?
I figured out the first part, but I can't figure out the second part. :(
Also,
It has to be a number? This is online homework and the answer is in the format:
F=_____W
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You'll want to find the acceleration of the person's center of mass during the jump. Use constant-acceleration kinematics. I don't recommend using the "no time" equation, but I'm not up for deriving it at the moment
(v_f)² - (v_i)² = 2a (x_f - x_i)
where "f" and "i" represent final and initial states, respectively. v_i = 0, we can let x_i = 0. That makes x_f = 0.41 m, and you say you know v_f. Solve for the acceleration
a = (v_f)² / (2 x_f)
Now use Newton's Second Law. Sketch a Free Body Diagram of the person while pushing on the floor. There will be a gravitational force mg downward, and a normal force N upward. Choose a coordinate system. I prefer positive accelerations, so I'll choose positive upward. Write out Newton's Second Law. I'll show signs explicitly, so symbols represent magnitudes.
Σ F = N - mg = ma
Solve for N
N = ma + mg
Since you want this in terms of the perosn's weight, divide both sides of the equation by mg.
(N / mg) = (ma / mg) + 1
The m's cancel on the right.
(N / mg) = (a / g) + 1
Neat question. I actually started answering it by saying there was insufficient information, but giving it more thought, I realized that it was OK.
(v_f)² - (v_i)² = 2a (x_f - x_i)
where "f" and "i" represent final and initial states, respectively. v_i = 0, we can let x_i = 0. That makes x_f = 0.41 m, and you say you know v_f. Solve for the acceleration
a = (v_f)² / (2 x_f)
Now use Newton's Second Law. Sketch a Free Body Diagram of the person while pushing on the floor. There will be a gravitational force mg downward, and a normal force N upward. Choose a coordinate system. I prefer positive accelerations, so I'll choose positive upward. Write out Newton's Second Law. I'll show signs explicitly, so symbols represent magnitudes.
Σ F = N - mg = ma
Solve for N
N = ma + mg
Since you want this in terms of the perosn's weight, divide both sides of the equation by mg.
(N / mg) = (ma / mg) + 1
The m's cancel on the right.
(N / mg) = (a / g) + 1
Neat question. I actually started answering it by saying there was insufficient information, but giving it more thought, I realized that it was OK.
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You're welcome. I'm glad to help.
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