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Normal Force While Going Up Stairs

  1. Dec 12, 2012 #1
    In my high school physics class, we are doing an experiment where we go up a flight of steps, record the time it takes, and calculate the work done in the vertical direction. I understand everything (I am a pretty bright student) except one part that I simply cannot wrap my head around.

    To calculate work, we use W = Fd, and to get F we use F = mg, finding our weight. I don't understand how we are moving upward if our normal force is equal to our weight. Isn't each person's normal force equal to their weight when they are just standing up without moving?

    My teacher tried to explain it to me, and he said that our normal force is greater than our weight when we jump, which would be an upward velocity. When we climb stairs we have an upward velocity, so how can the normal force be equal to our weight? Thank you for helping!
  2. jcsd
  3. Dec 12, 2012 #2
    I think the calculations you are doing are leaving out the way people normally walk up stairs; one leg at a time.

    Imagine if you didn't walk up one leg at a time. You would be jumping. So for the sake of the experiment, where work and energy are the issues being studied, you're ignoring the human body's design and function.

    I think one's quadriceps would apply work in this case and could be analyzed for normal force and such. But when looking at it from the point of view of a 'Point A' and 'Point B' this is not relevant.

    There must be a split second where the calf/upper leg muscles raise the rest of the body. But your experiment is not analyzing that.
  4. Dec 12, 2012 #3


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    Welcome to the PF. You will enjoy this place.

    The normal force as you walk up stairs varies above and below F=mg, but the average is pretty close if you are moving up the stairs at a constant velocity. Does that make sense?
    Last edited: Dec 12, 2012
  5. Dec 13, 2012 #4
    The normal force exerted by the stairs on you is very close to your weight, but slightly higher. But this force is not moving through a distance. What is that all about? Even though the force is not moving through a distance, the center of mass of your body is. Your center of mass is moving upwards. And that is what really counts. This force exerted by the stairs is pretty much transmitted through your body to your center of mass (unless your body rotates, which it doesn't). This is how it does work. The force exerted by the stairs times the distance traveled by your center of mass is equal to the amount of work the stairs does on you. Your body first converts chemical energy from the food you eat into this mechanical work by allowing you to move upward under the force exerted by the stairs. So the chemical energy is being converted to mechanical energy, and the mechanical energy is being converted into gravitational potential energy.
  6. Dec 14, 2012 #5


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    Or when moving up at a constant speed, like in an elevator. When climbing stairs at a constant average rate per gait cycle, the average normal force will also be equal to the weight.
  7. Dec 14, 2012 #6
    The reason that this question is a little tricky is that the human body is not a rigid body like we are often used to. Different parts of the body are moving in different speeds and directions at the same time.

    Here is a simple example to give you a better feel for what is happening. Imagine a frictionless cylinder in which a piston of mass m is present. The cylinder axis is vertical, and the cylinder is sitting on the ground. There is a compressed massless spring between the piston and the ground within the cylinder, and there is a massless dashpot (shock absorber) also connected between the piston and the ground (running down the middle of the spring). The spring is initially held in compression by a constraining strut. But, at time = 0, the strut is suddenly severed, and the spring is then free to expand. In what we are going to do, we are going to regard the combination of spring, dashpot, and piston as an analog to the human body. Before the strut is severed, there is a downward force on our combined body equal to the weight of the piston, and an upward force on our combined body at the floor (base of the spring), also equal to the weight of the piston. Once the strut is severed, the spring begins expanding and the piston moves upwards. The force between the floor and the base of the spring becomes higher than the weight of the piston. But the base of our body does not move. The severing of the strut and release of the spring is analogous to us using some of our stored chemical energy to create mechanical work. The center of mass of our combined body moves upward, even though there is no movement at the contact point between the ground and our combined body. Eventually, the center of mass of our combined body will settle at a higher elevation than originally.
  8. Dec 15, 2012 #7


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    The work is just the useful part of the energy that has been exhausted. The excess energy it takes for you to jump up the stairs is wasted. Technically, it takes work to propel your body upwards faster than gravity, but then when you land, that energy gets dissipated, so it doesn't count as work going up the stairs.
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