# Forces acting on a static trolley suitcase

• lavoisier
In summary, a trolley suitcase has a weight that causes it to spin if it is not held upright, but the weight does not increase as the angle decreases.
lavoisier
Hi everyone, a very simple problem that is nevertheless baffling me, probably because I'm no physicist and I lack method in tackling it.
A few days ago I was on my way home from the airport, and I was carrying a trolley suitcase, a bit like this one:

The suitcase weighed about 10 kg, but it occurred to me that when I stopped (with the suitcase still tilted at an angle, not resting vertically) the weight acting on my hand was surely much less than 10 kg.
When I got home, I got out that little thingy that you use to weigh suitcases (a sort of dynamometer?), I attached it to the handle (fully stretched out) and tilted the suitcase at various angles from the ground, checking the corresponding weight.
If you measure the angle between the ground and the line passing through the handle and the wheels touching the ground, at 90° of course there was no weight because the suitcase was resting. Still no weight at a particular angle a bit smaller than 90° (probably at the point where the centre of gravity lay on the vertical line from the wheels), then increasingly larger weight (up to about 4 kg) as the angle decreased to about 50°, I reckon. What surprised me was that the weight didn't increase any further. I was expecting it to get larger and be maximal at a very small angle.
I reasoned that the weight of the suitcase acts on its centre of gravity, which is probably close to the geometric centre of the 'main' body. The suitcase is static when this weight is balanced by the reaction of the ground plus the force exerted by the person on the handle. What I can't figure out is how the various forces distribute and where they act. For instance, I think I remember from physics I at university that the reaction from the ground always acts vertically. But then, wouldn't that completely counterbalance the weight, which is also acting vertically? What component of the weight causes the suitcase to spin and fall if you don't hold it? Etc.

So, could anyone please point me to some information concerning the static forces acting on a trolley suitcase (or a related case) depending on the angle it forms to the ground?

Thanks!
L

How did you measure the force for angles up to 50 degrees?
If you incline the suitcase by a small angle, it will have the tendency to go back to vertical. So you need a force pushing down and not up. After it reaches the angle at which it has the tendency to fall rather than going back, the force to keep it from falling should be constant (about 1/2 the weight).
This is assuming that there is enough friction to stop it from sliding horizontally. Which is not the case always.

Thank you both for your replies. I'll read more on the subject and see if I can figure things out.
I think my main difficulty is understanding how the split the various forces into components. I suppose the points where wheels touch the ground form the rotational axis, so any force acting perpendicularly to this axis doesn't constitute a torque. If I draw a line L from the centre of gravity and perpendicular the rotational axis, I can split the weight into a component W1 along L and one W2 perpendicular to it. W2 should be responsible for the tendency of the suitcase to rotate. W1 instead should be the part that is just balanced by the reaction of the ground. This is where I get confused, because I think the reaction should be vertical, but W1 is not. I'll think about it.

@nasu: the suitcase tended to go back to vertical only between 90° and the angle (75°?) where a sort of unstable equilibrium was reached. After that, the handle always 'pushed' down. Is this in contradiction with the theory? The wheels didn't slide; I tried again just now with the empty suitcase, same story.

## 1. What are the forces acting on a static trolley suitcase?

The main forces acting on a static trolley suitcase are the weight of the suitcase, the normal force from the ground, and the friction force from the wheels.

## 2. How does the weight of the suitcase affect the forces acting on it?

The weight of the suitcase creates a downward force known as the force of gravity. This force is counteracted by the normal force from the ground, resulting in a balanced force system.

## 3. Why is the normal force important in this scenario?

The normal force is important because it is the force that supports the weight of the suitcase and prevents it from sinking into the ground. It also helps to keep the suitcase in a stable position.

## 4. How does friction affect the motion of a static trolley suitcase?

Friction is the force that resists the motion of the suitcase. In the case of a static trolley suitcase, the friction force from the wheels helps to keep the suitcase in place and prevent it from rolling or sliding.

## 5. Can the forces acting on a static trolley suitcase change?

Yes, the forces acting on a static trolley suitcase can change if external forces are applied, such as someone pushing or pulling the suitcase. This can result in a different force system and potentially cause the suitcase to move.

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