People run faster than they walk

[black_squirrel]

Homework Statement

People can run much faster than they can walk. Why is it so? Estimate the maximal
walking speed for a man, height 175 cm, and for a 7 years old child, height 120 cm. (A hint: In the first approximation, the legs of a walking person do not bend, and their length is about half of his height.) Estimate how fast you would be able to walk at the Moon, where gravity force is 6 times weaker.

The Attempt at a Solution

When I first read this question, it seemed trivial but I don't see how I can estimate a maximal walking speed. It obviously depends on the rate at which the person steps but as you increase the rate, you end up running...so I'm not sure what this question is getting at. Help please!

 

[Kurdt]

bit of a strange question but if you assume a person can take one stride in one second, then how far will that stride be? This will also give you an easy way of working out the walking speed which is simply the distance traveled with 1 stride per second. Since the legs don't bend they will be two sides of a triangle.

 

[black_squirrel]

bit of a strange question but if you assume a person can take one stride in one second, then how far will that stride be? This will also give you an easy way of working out the walking speed which is simply the distance traveled with 1 stride per second. Since the legs don't bend they will be two sides of a triangle.

but it doesn't make sense to me to just pick an arbitrary rate. this question is wack. I'm thinking maybe if i could figure out a way of incorporating the person's weight into it...since the second part asks the speed on the moon..?

 

[Kurdt]

Actually I was kind of interested in this because I hadn't come across it before and it was a bit unusual. My approach is probably too simplistic. If one considers the motion of the hip it will move in circular arcs much like a point on a rotating circle (a cycloid). In this fashion one can equate two forces one of which contains the acceleration due to gravity and the other the speed of motion.

One can assume at the top of the cycloid that the centripetal force is equal to the weight to be at the point where the foot remains on the ground and thus satisfies the condition of walking. This assumption gives the maximal walking speed of course.

I hope that's clear I'm doing many things at once.

 

[black_squirrel]

Actually I was kind of interested in this because I hadn't come across it before and it was a bit unusual. My approach is probably too simplistic. If one considers the motion of the hip it will move in circular arcs much like a point on a rotating circle (a cycloid). In this fashion one can equate two forces one of which contains the acceleration due to gravity and the other the speed of motion.

One can assume at the top of the cycloid that the centripetal force is equal to the weight to be at the point where the foot remains on the ground and thus satisfies the condition of walking. This assumption gives the maximal walking speed of course.

I hope that's clear I'm doing many things at once.

oh wow, i hadn't thought of that. I'm not exactly sure what two forces you're suggesting should be equal. I'd really appreciate it if you could explain this a little bit more.

 

[Kurdt]

Well centripetal force is one I've stated explicitly. and the weight is the other force. At the top of the hips circular arc these two will be equal in maximal walking motion. I can't give you what they are since I'll have done your homework for you which is not the policy of this forum. But if you google each term or look them up in a general physics text you'll be able to find both.

 

[black_squirrel]

oh sorry. i guess what I really wanted to ask was when you say "One can assume at the top of the cycloid that the centripetal force is equal to the weight to be at the point where the foot remains on the ground and thus satisfies the condition of walking." I don't see the reasoning behind your assumption. I'm sure it's right but at what point in the walking motion is the centripetal force equal to the weight of the person?

 

[Kurdt]

Since the hips are moving in circular arcs with the same radius of the leg, the maximal speed of walking would be when the centripetal force is balanced with the weight of the person. If the centripetal force was greater than the weight the persons foot would leave the floor and this is not walking. We choose the two to be equal to give the maximal walking speed because this is what is asked for. Of course in real life the centripetal force would probably be less than the weight but that's not what the question asks.

 

[chaoseverlasting]

I don't think its that complicated. You have to take friction into account. Thats how the weight of the person comes into play (the normal reaction more precisely). Friction is the driving force here, as its that which gives you your forward motion.