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This is not a homework question. I attempted to draw a free body diagram for a person pulling or pushing a cart.

Based on Newton's third law, the following forces act on the body of the person:

  • forward reaction force done by the ground because of friction between the person and the ground.
  • downward force (the person's weight) done by the earth.
  • backward reaction force done by the cart.

I am wondering why the body of the person must be tilted forward. I have not seen any relationship between this posture with the magnitude of the forces acting on the person.

Could you tell me why the person's body must be tilted forward? How does this posture provide mechanical advantages?

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    $\begingroup$ Does this answer your question? Which is easier, pushing or pulling? $\endgroup$
    – AlphaLife
    Commented Sep 8, 2021 at 6:27
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    $\begingroup$ Am I the only one who's wondering why the lady in the first drawing is chained from her ankle to the right side of the image? That might also affect how well she can push the cart... $\endgroup$
    – ilkkachu
    Commented Sep 8, 2021 at 9:05
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    $\begingroup$ haha that made me laugh more than it should have $\endgroup$
    – franz
    Commented Sep 8, 2021 at 11:22
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    $\begingroup$ @ikkachu: Original image has her chained to an iron ball labeled DEBT. $\endgroup$
    – Ross Presser
    Commented Sep 8, 2021 at 13:11
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    $\begingroup$ @MakeMeSmarterEveryDay in the simplest sense, if you stood perfectly upright with a cart in front of you, gave it hard shove away from you (let's call that "forwards"), what would happen to you (imagining that you take no steps or anything, just stand, shove, accept consequences)? $\endgroup$
    – Caius Jard
    Commented Sep 8, 2021 at 13:38

6 Answers 6

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It adds a horizontal component to the vertical force exerted by your legs.

When you're standing straight up, the forces exerted by your legs are straight up and down. Your legs are designed to exert a force to counter your bodyweight and allow you to stand like this, so they're quite strong at countering this force.

When you're leaning over like this, each step you take restores you a leaning version of standing straight position, and it allows you to exert this standing-up force your legs exert in a horizontal direction - in each of these pictures, you can see the person with one leg straight back, and the other bent in front of it; at the completion of each step, you could consider them to be standing with both legs straight back for a brief moment before they move the next leg.

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    $\begingroup$ Exactly, the reasons for leaning are as much biomechanical as they are physics. It also enables your spine and skeletal system to absorb much of the impact instead of requiring your muscles to compensate. $\endgroup$
    – bta
    Commented Sep 9, 2021 at 1:09
  • $\begingroup$ Doesn't it also direct some of the person's weight towards pushing/pulling? e.g. if you have a wheel touching a perfectly vertical plank of wood the wheel will not start rolling but if friction etc. on the wheel is low enough you could make the wheel move by leaning the plank against it at low enough angle. $\endgroup$
    – jwezorek
    Commented Sep 10, 2021 at 17:08
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Probably the easiest way to analyze it is in terms of torque balance.

So, you already know that a rigid body which happens to have a constant momentum, this constancy requires all of the external forces to sum to zero: this is force balance. (It is sometimes confused with Newton's third law; Newton's third law just says here that “You don't need to consider all the forces, only the external ones. The internal forces cancel each other out.”)

Well, the same thing can be said of any conserved quantity, it doesn't just have to be momentum. If my sink is a bit clogged and there is a standing water level in my sink, conservation of mass of the water is going to guarantee that if the water level is not changing, then water coming in from the faucet is equally balanced by water leaving, either by evaporation or by slipping around the clog. There is a state of water flow balance. All of these balances are called “dynamic equilibrium” conditions.

The conserved quantity that matters in the torque case is called angular momentum, torque is a property of force that can transfer angular momentum, and if we notice that a human is staying constant orientation, then we can conclude that they are in a state of torque balance.

Once you know to look here the rest of the analysis is very straightforward. The forces are roughly comparable: the horizontal component to force on the feet always points forwards when walking forwards and has to provide also the horizontal component to force on the cart. The cart’s reaction force on the person is thus backwards, the force on the feet is forwards, and they are about the same magnitude. Torque says we should multiply by the lever arm, which is to say the distance from about this person's belly button where the line of the force intersects them. The problem is that the force on the feet is about as far as it can be, whereas if I'm grasping something with my arms at about waist level, that's about as close to my center of mass as it can be. So the torque from my legs might easily be 10 times the torque of the weight that I'm pulling.

The leaning forward allows the person to use gravity to counter the torque.

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    $\begingroup$ As you have the accepted answer -> a little diagram would make a world of a difference. ;) $\endgroup$
    – AnoE
    Commented Sep 9, 2021 at 14:27
  • $\begingroup$ Really nice answer. $\endgroup$
    – Árpád Szendrei
    Commented Sep 9, 2021 at 21:20
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    $\begingroup$ I think the torque argument is not exactly right: it should be about how gravity (acting on center of body mass) and normal force (acting on feet) don’t align when leaning forward. When standing up straight they align, adding net zero to the total torque on the body (regardless of the center point of rotation, which we are free to choose; doesn’t need to be center of mass!) thus making it impossible to push forward without tilting over backward. The height of pushing (belly button or eye height) doesn’t make a fundamental difference. $\endgroup$
    – mvds
    Commented Sep 11, 2021 at 19:00
  • $\begingroup$ You're absolutely right, and I keep looking at this answer again and being like, there's actually an inconsistency here: pedagogically I find it very useful to put the pivot point at the center of mass and then the normal force does the torque, not gravity (which cannot do a torque as it operates on the center of mass)... But in terms of how I actually think it through, I put the pivot at the feet because those are the forces I don't know and so it's handy to zero out their torque, driving the above explanation that it's gravity what torques ya. $\endgroup$
    – CR Drost
    Commented Sep 12, 2021 at 10:20
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It's about acceleration.

enter image description here

You don't need to pull a load behind you. You see this when you wish to accelerate significantly1 and not fall down.

enter image description here

If you aren't accelerating you shouldn't be leaning (or you'll fall over). At the end of a long enough race you'll be going as fast as you can. So no more accelerating. No more leaning. 2

enter image description here

As you move through a curve you accelerate towards the center of the curve. To avoid falling over you lean into the curve.

enter image description here

If you aren't accelerating you don't need to lean. You can be moving as fast as you like. So long as your speed isn't changing there is no acceleration and so no leaning.

enter image description here

You can prove this to yourself by balancing a stick on your hand. Let it lean in any direction and to return it to balance it you'll have to accelerate it in the direction of the lean.

Do that on a moving train or a flying plane and you'll find the stick behaves the same way. Unless you're experiencing turbulence (which is also acceleration) the stick will behave the same as it did when you were standing still.

enter image description here

But do this in space and the leaning is no longer a thing. That's because you need gravity for leaning to mean anything. It's the pull of gravity that gives you potential energy that you can turn into horizontal kinetic energy as you fall over. When you lean against acceleration you're using that to keep yourself balanced.

enter image description here

It should be understood that leaning doesn't add a continuous source of energy. Rather it lets your legs work both vertically and horizontally. Vertically you lose and recover potential energy as your legs work. The leaning turns that energy into forward acceleration. Horizontally, your legs simply push you forward. Something they can't do if you stand upright. At least, not without walking out from under you.

enter image description here

You may feel the leaning seems more pronounced with the heavy cart. There is a good reason for that. A cart adds mass you can't lean. So you have to lean more for longer to get to the same speed. That's because the added mass adds inertia. That's why leaning while accelerating a heavy cart looks so much more dramatic. Even when the ground is level. With the added mass that you can lean further and have more time before the acceleration ends.

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    $\begingroup$ Great use of photos to display answer. $\endgroup$
    – JosephDoggie
    Commented Sep 8, 2021 at 20:18
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    $\begingroup$ Acceleration and force aren't the same thing (acceleration depends on net force). Friction provides a force which must be countered, and leaning helps counter that even when not accelerating. $\endgroup$
    – Acccumulation
    Commented Sep 8, 2021 at 21:10
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    $\begingroup$ @user3067860 I'll encourage you to consider the difference between these two questions: What? vs How Much? Leaning can counter a force that if not countered would make your body rotate and fall over. However when that is a small force it only requires a small lean. Small enough and your stance or even just your feat and toes can negate the tendency to rotate. You can prove this to yourself by pushing a cardboard box across a hardwood floor. It will only rotate if it is either too tall or you push fairly violently. Tilting the box helps in some cases but in some it's not needed. $\endgroup$
    – candied_orange
    Commented Sep 9, 2021 at 14:25
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    $\begingroup$ @user3067860 because I'm modeling you as a stick not a box. Stand your car on it's bumper and put it on a hover board on level ground and all the leaning stuff will happen. There is no statement so sound that someone can't find a context to put it in that will make it absurd. Just because Newton didn't give us relativity doesn't mean his lessons are useless. I'm sorry but there simply isn't room here to cover every corner case. All I can offer is a Lie to Children $\endgroup$
    – candied_orange
    Commented Sep 9, 2021 at 15:17
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    $\begingroup$ @user3067860: When a car accelerates hard, it does tip because of the forces involved. e.g. when braking hard, the hood dips. In powerful cars accelerating forward from a standstill, there's some raising of the hood. If cars weren't already very stable with a low centre of gravity, and wheels far in front and behind that centre of gravity (e.g. a giant mech with wheels instead of feet), then this tipping force would put them into an unstable state and they'd fall down if they didn't proactively lean before accelerating. $\endgroup$
    – Peter Cordes
    Commented Sep 10, 2021 at 7:26
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You do not want your body to rotate.

The forward friction force wants to rotate your body backwards.

You tilt your center of mass forward so that the normal force supplies a counter-balancing torque that wants to rotate your body forwards. The two torques cancel and your body is in rotational equilibrium.

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    $\begingroup$ No problem. Note that there is also a force pushing or pulling on the body from the cart. In all your diagrams, this force is close to the CG, so it doesn't supply much of a torque about the CG, so I neglected it in my answer. My answer would be a good response to "Why must you lean forward when sprinting?" $\endgroup$
    – Evan
    Commented Sep 7, 2021 at 16:33
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It's similar to why when you pull something with a rope along the ground it can never be vertical. It needs to have a horizontal component to apply a horizontal force.

This is not quite as true with rigid structures like legs, but it similar in that it reduces bending stresses on the leg bones and torques on you knees and hips. It effectively reduces the lever arm formed by our legs between our hips and feet which increases the force that can be applied. A wheel (a round lever) is an example of where this does snot happen: a straight lever that pushes parallel to the ground while being perpendicular to it.

If you calculate the internal forces on the leg bones and the force/torque at the joints, you will find the differences. What you're doing right now is similar to calculating the force at the edge of a large and small wheel and being unable to find the difference. The difference is the torque at the shaft.

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    $\begingroup$ Also, since the person performing the work does so at an angle, wouldn’t some component of the force he applies reduce the normal force exerted by the ground, hence reducing the work required due to less work against friction (basically the same logic as to why in most cases it’s easier to pull an object than to push it)? $\endgroup$
    – m-Xylene
    Commented Sep 7, 2021 at 16:02
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    $\begingroup$ @m-Xylene Are you talking about traction? The angle reduces normal force due to weight but is more than made up by the fact you have something to push against. Most obvious when on soft earth and you actually dig into the ground. Or you mean because the object is being pushed up slightly so reduces its friction? $\endgroup$
    – DKNguyen
    Commented Sep 7, 2021 at 16:03
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    $\begingroup$ That too, but what I meant was that since friction = $\mu \ N$ where N is the normal force, and we can assume in most cases $N = mg$, if an oblique force was applied with a component in the y-direction (upward) then it would become $N + F cos\Theta = mg$ thereby decreasing N and thus the frictional force, which would conserve a small amount of energy, correct? $\endgroup$
    – m-Xylene
    Commented Sep 7, 2021 at 16:06
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    $\begingroup$ @m-Xylene I guess but I find the corner digging in to outweigh the benefit there. $\endgroup$
    – DKNguyen
    Commented Sep 7, 2021 at 16:07
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    $\begingroup$ @m-Xylene Well, OP was asking about wheels not block so the lifting and digging in is moot. I disagree with the pulling being intuitively better. It just lets you see what is in front and lets you have long pull arms for better torque to steer. I think pulling is more about the eyes and arms. Wheelbarrows have rear steering arms but our joints require more of a lifting than pushing action there. $\endgroup$
    – DKNguyen
    Commented Sep 7, 2021 at 16:13
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It could not be easier to explain this.

Using your diagrams:

You're trying to move the cart left or right - not up or down.

So ............. you have to push left or right.

It's that simple.

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