Calculating Time to Catch a Falling Baby: SQRT2 & Height

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Homework Help Overview

The discussion revolves around calculating the time it takes for a baby to fall from an upright position, specifically questioning the applicability of the formula involving the square root of height and gravitational acceleration. Participants explore the dynamics of the fall and the assumptions regarding the baby's initial position.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the implications of the baby's starting position on the fall time, questioning whether a perfectly upright position would result in no fall. There are considerations of using energy conservation principles versus kinematic equations to determine the fall time.

Discussion Status

The discussion is active, with various interpretations being explored regarding the forces acting on the baby and the conditions under which it would fall. Some participants suggest drawing diagrams to visualize the problem, while others note the complexity of calculating time compared to velocity.

Contextual Notes

There is an ongoing debate about the assumptions made regarding the baby's initial angle and the forces involved in the fall, particularly the role of gravity and the baby's center of mass. The discussion acknowledges the challenge of calculating time versus velocity in this scenario.

peripatein
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Hi,

If a baby learning how to walk loses balance and falls sideways from an upright position (whilst standing), how long before the baby hits the ground, i.e how much time does one have to catch the baby?
Is the time in that case still equal to SQRT(2*baby's height/9.81)?
 
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I think an assumption would have to be made about it's starting position.

If the baby happened to be standing perfectly straight up when it started to fall there would be no force pulling it over. So as it's starting position tends towards vertical the time taken to fall appears to approach infinity.
 
The question is formulated thus: "a baby learning how to walk loses balance and falls aside (from an upright position). Which parameters determine the time of its fall?" Should I use energy conservation instead, i.e potential equals kinetic, and then Vt = 1/2*g*t^2, for finding t?
 
As I said. If the baby is dead upright, why would it fall? What is the force pulling it sideways? Gravity only acts downwards.

Perhaps try drawing the set up. Assume baby is hinged to the floor at his feet. Have him leaning at say 10 degrees. Assume gravity acts on his center of mass. Work out the force causing him to rotate about his feet. What happens to that force as the starting angle approaches zero?
 
PS Using KE=PE to calculate the velocity with which he hits the floor is possible but calculating the time taken is a harder problem.
 

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