Surviving a Fall: Calculating Velocity and Impulse for Safe Landings

[jakeowens]

While constructing a space platform a 90-kg robot finds itself standing on a 35-m long 205-kg steel beam that is motionless with respect to the platform. Using its magnetic feet it walks along the beam traveling south relative to the platform at 1.85 m/s. What is the velocity of the beam with respect to the platform as the robot walks?

For this question, i assumed that the KE of the robot and the beam would be equal. (is this a correct assumption?) So on using that, i found out the KE of the robot through 1/2mv^2, and came up with 154.0125J. Since for every action there is an equal and opposite reaction, i could say that the kinetic energy of the beam was also 154.0125J. From there, i did some simple algebra solving for V, and came up with the beams velocity being 1.226m/s. Am i correct here?

A person can just survive a full-body collision (either to the front, back or side) at roughly 9 m/s (20 mi/h) with an impact time of approximately 10 ms. At greater speeds or shorter times, fatal brain damage will likely occur. Could someone survive a fall from a 4 m landing flat on his or her back on soft soil so that s/he decelerates to rest through a distance of 10 cm (that's the total compression of the body and soil)? (Hint: survival depends on the magnitude of the deceleration, not on the impact time.) Will they survive?

If his or her mass is 51 kg, what's the impulse exerted on his or her body by the ground? Assume the deceleration is constant.

For this problem, i'd have no trouble doing it but the fact that they decelerate to rest in 10cm throws me off. I don't know quite how to account for that in my formulas.

I used delta S= Vi*t+1/2at^2 and came up with t=.903seconds, and then plugged that into vf=vi+at to find out that their final speed was 8.858m/s, but I'm not sure if I'm on the right track because i don't know how to factor in the 10cm that they (and the soil) compress when they hit.

So according to this, they would survive, but I'm not sure where to go with this next. I just need help figuring out what to do with that decelerating in 10cm part. Or if I'm totally off base here i need a lot of help.

Thanks

 

[mezarashi]

For the first part, your assumption is not correct. There is no reason for it to be. The correct principle to apply would have been the conservation of momentum since the beam-robot system is isolated (no external forces). Momentum is always conserved and thus it is always safe to assume this if it makes solving the problem easy.

The problem is oddly worded however. If the robot continued to "walk on" the beam it would in fact be accelerating but is not indicated in the problem. So essentially then it is asking. If the robot had accelerated itself by pushing on the beam and is now moving to the right, what is the velocity of the beam to the left to conserve momentum?

 

[mezarashi]

For the second problem, there are several parts

The information given was to tell you that a person can take so much acceleration. a = v/t. If the acceleration is too great, he or she will suffer injuries. Your objective is then to find the acceleration of the person in a collision.

First part, find the person's velocity just before impact. This will then become your initial velocity for the next part

Now you start a new kinematics analysis. You know initial velocity and final velocity. You know displacement. 3 knowns, apply one of the big four for acceleration. (hint: vf^2 = vi^2 + 2ad)