# Why does mass have no effect on stopping distance?

• samdiah
In summary: So mass does indeed affect stopping distance in a very simple model like two blocks of different masses.
samdiah
Why does mass have no effect on stopping distance?

Who said it didn't? What assumptions are you making here? If a mass, m, traveling at speed v, is opposed by a constant force F, then F= ma so a, the acceleration (which is negative since F is negative) is F/m and the mass will stop when v- (F/m)t= 0 or when t= mv/F. In that situation the stopping time is proportional to the mass. Is your question about a special situation?

Maybe you are simply looking at the kinematics equation. In that case, you are already given acceleration and hence mass may seem to have no effect on the stopping distance. When in fact it does, as HallsofIvy have demonstrated.

hey my first post, try to think of it like this...
A car and a truck DONT have the same stopping distance when initally going the same speed, it maybe possible to have the same stopping distance if you have big brakes on the truck. Ffriction=(mu)*(Normal), so the larger the mass (normal becomes larger) the more frictional force you need (bigger brakes)...
Hence mass Does indeed affect stopping distance.
Hope that helps.

I am looking at a situation where one mass is double the other mass, and the kenetic energy and force were constant or same for both.

Thankyou everyone

assuming they have the same coefficient of friction, i don't see why the lighter one would stop any faster than the heavier one.

F = (mu)N = ma
N = (mg)

Well, if you look at N = mg, and if you noticed m in there, the mass actually influences the N, which influences the F, which changes the aceleration...

From F=ma =>larger mass smaller deceleration.
From F=(mu)N => larger mass, larger Normal force, smaller deceleration.

the m's don't cancel out, if that is what you are implying because that would mean the forces that you are comparing are different.

QuantumCrash said:
Well, if you look at N = mg, and if you noticed m in there, the mass actually influences the N, which influences the F, which changes the aceleration...

From F=ma =>larger mass smaller deceleration.
From F=(mu)N => larger mass, larger Normal force, smaller deceleration.

the m's don't cancel out, if that is what you are implying because that would mean the forces that you are comparing are different.

the m's do cancel out, though. the equation reads (mu)*m*g = m*a, solving for the acceleration you get a = mu*g. this came up in physics 1 a few years ago and i was super confused.

of course if there is a braking force applied (not just coasting to a stop) then it's true the lighter one is easier to break. this would also be ignoring air resistance, which would complexify things even more.

teclo said:
the m's do cancel out, though. the equation reads (mu)*m*g = m*a, solving for the acceleration you get a = mu*g. this came up in physics 1 a few years ago and i was super confused.

Yes, that does make sense. My mistake. Larger normal force, larger friction. So mass does not affect stopping distance in a very simple model like two blocks of different masses.

However, in the case of the truck and the car, friction from the ground contributes only a small proportion of the stopping force. Most of it is provided by air resistance, friction within the system, etc.

## 1. Why does increasing the mass of an object not affect its stopping distance?

According to Newton's second law of motion, the force required to stop an object is directly proportional to its mass and acceleration. However, when it comes to stopping distance, the deceleration of the object is also taken into account. Since an increase in mass also leads to an increase in inertia, it requires a greater force to decelerate the object, resulting in a longer stopping distance.

## 2. Is there any scenario where mass can affect stopping distance?

Yes, there are certain scenarios where mass can have an impact on stopping distance. For example, in a collision between two objects, the object with a greater mass will experience a smaller change in velocity and therefore a shorter stopping distance compared to the lighter object.

## 3. Does the shape or size of an object affect its stopping distance?

Yes, the shape and size of an object can also have an effect on its stopping distance. Objects with larger surface areas experience more air resistance, which can slow down the object and increase its overall stopping distance.

## 4. How does friction play a role in stopping distance?

Friction is a force that opposes the motion of an object. When an object is moving, the force of friction acts in the opposite direction, causing the object to slow down and eventually come to a stop. Therefore, the amount of friction between an object and its surroundings can affect its stopping distance.

## 5. Can other factors besides mass affect stopping distance?

Yes, there are several other factors that can influence stopping distance, such as the surface condition, the type of surface, and the speed at which the object is moving. For example, a wet or slippery surface will increase the stopping distance, while a rough surface will decrease it. Additionally, a higher speed will require a longer stopping distance compared to a lower speed.

• Introductory Physics Homework Help
Replies
24
Views
2K
• Introductory Physics Homework Help
Replies
31
Views
2K
• Introductory Physics Homework Help
Replies
14
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
3K
• Introductory Physics Homework Help
Replies
12
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
336
• Introductory Physics Homework Help
Replies
13
Views
906
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
10
Views
653
• Introductory Physics Homework Help
Replies
5
Views
862