Pulling force required to get stationary vehicle moving

Question

Background

There are many examples from humans pulling heavy vehicles, ranging from trucks to airliners. When researching the physics behind this, most results pointed to the reduced rolling resistance when the vehicles are on wheels. Because the normal force of the vehicle is multiplied with the rolling coefficient, which is about 0.02 for tires on asphalt, the force in the horizontal direction opposite to the direction of travel greatly reduces. However, I am confused about how this compares with the concept of static friction. My current interpretation is that the rolling resistance only applies when the vehicle is already moving, and that one has to overcome static friction to get from stationary to moving? And the static friction has a coefficient much closer to one so would that initial force to overcome the static friction be much higher?

Problem formulation

So, let's assume there is a vehicle of mass $m$ on rubber wheels, standing stationary on asphalt. A rope is attached to the vehicle in the direction of moving/the wheels. Neglecting friction in the internal car systems, how does one compute the force required by a human pulling on the rope to get the car moving? Is the required pulling force equal to the static friction, i.e. $F_{pull}=\mu mg$? After which the force required to keep the vehicle moving at constant speed is equal to the rolling resistance $F=cmg$? Also, is there some common value for the 'pulling strength' of a human to compute how many it would take to get a vehicle moving?

Answer 1

There is a difference, obviously, between static friction and rolling friction. Static friction is required to give the wheel speed when a torque is applied to it. When the wheel has reached a certain velocity and moves with a constant velocity (when the torque doesn't apply anymore), then in the ideal situation (where no kinetic energy of the wheel is converted in some other energy form), the wheel will keep rolling forever experiencing no static friction anymore (which it felt only during the acceleration caused by the torque).
The situation, however, is far from ideal. Energy is dissipated. And it's here where the rolling friction comes into play. The rolling friction causes the wheel not to accelerate, as static friction does, but to decellerate the wheel. The torques have opposite directions in both cases but do not have the same value.
To start the wheel moving you can apply a force (torque) until a certain limit is reached. When a force (torque) with a value above this limit is applied, the wheel experiences kinetic friction (the wheel experiences friction with the surface which it's on; look at the smoke in the accelerating Formula 1 racing cars at the start, although accelerating with static friction would be more efficient, all drivers give just full gas).
When the torque is not applied anymore, the wheel will decelerate. This is caused by the rolling friction.

Answer 2

My current interpretation is that the rolling resistance only applies when the vehicle is already moving

That is correct.

and that one has to overcome static friction to get from stationary to moving?

That is not correct. Although there is a small static friction force that resists the beginning of rolling motion, it is generally too small to make a difference. Instead static friction prevents relative motion between the tire surface and the road, i.e., skidding or sliding. The force of static friction prevents the wheel from sliding and thus allowing the wheel to roll forward. It does not oppose rolling motion.

And the static friction has a coefficient much closer to one so would that initial force to overcome the static friction be much higher?

Closer to one than what? If you mean the coefficient of rolling resistance, than yes. Rolling resistance is the force that opposes rolling at constant speed over a surface. According to Wikipedia the rolling resistance of most new passenger tires is in the range 0.007 to 0.14 so it is generally much less than the coefficient of static friction. But again, the initial pulling force does not have to overcome static friction.

Problem formulation

Neglecting friction in the internal car systems, how does one compute the force required by a human pulling on the rope to get the car moving?

"Getting the car moving" means accelerating the car. The pulling force required to accelerate the car is calculated based on Newton's second law

$$a=\frac{F}{m}$$

Is is the required pulling force equal to the static friction, i.e. $F_{pull}=\mu mg$?

No, $umg$ is the maximum possible static friction force. The force required to accelerate the care is per Newton's second law as stated above.

After which the force required to keep the vehicle moving at constant speed is equal to the rolling resistance $F=cmg$?

That is correct, where $c$ is the coefficient of rolling resistance (CRR).

Also, is there some common value for the 'pulling strength' of a human to compute how many it would take to get a vehicle moving?

According to the Canadian Centre for Occupational Health and Safety, where a worker can support his body (or feet) against a firm structure he can develop a force of up to 675 N. Assuming this is applied to a small 1000 kG vehicle then according to $F=ma$ an acceleration of up to 0.675 m/s$^2$ would be possible. For comparison, a car accelerating from 0 to 60 mph in 5.9 sec has an acceleration of 4.5 m/s$^2$

Hope this helps.