Newtons Laws with mouse and elephant

1. The problem statement, all variables and given/known data

A mouse and an elephant are on a perfectly flat ice rink (no friction). 10N of force is applied to each animal for 10 seconds, describe their behaviour.

2. Relevant equations


3. The attempt at a solution

Both animals will accelerate immediately and continue accelerating for 10 seconds with the mouse accelerating at a faster rate than the elephant. After 10 seconds both animals will continue to move with constant velocity
Thanks, but I still dont get it.
I was told that not being able to move a bus with your hands, but able to push a bike with your hands was because of a difference in inertia of the 2 objects.
Isnt this only because they have different frictional forces and nothing to do with any difference in inertia ???
The heavier object has a larger mass, thus a larger inertia. In other words, the bus can resist to any changes of motion better than the bike. The reason why the frictional force on the bus is larger than on the bike, is that the bus has a larger mass.

F.friction=my*N (Where N=mg on a flat surface)

As I see it, it's like attacking the same problem from different angles. Your explanation is fine in my opinion.
Just to clarify

Am I right in saying that a bus can be moved immediately (with small but increasing velocity) with the lightest touch if there was no friction, despite its huge inertia ??
Yes. The bus will start moving. Let's take an example. We have your 25 000 kg bus, and a 10 kg bike in space.

Now we exert a force of 2 N on both bodies. If we assume that we can neglect all opposing forces, (i.e. there is no friction, and gravitational forces are minimal) we can easilly calculate the acceleration the bus will get, and the acceleration the bike will get from

F=ma --> a=F/m

We see that the bus will get a smaller acceleration because it has a larger mass. In other words, when we stop applying our 2 N force on the bodies, the bike will have a larger velocity. That's what inertia is about. The heavier bus will not change it's state of motion as much as the bike. It's about comparison. Light object will get larger velocities than heavier objects when an equal force is applied on both bodies.

So back to your question, the bus will start moving with the lightest touch, but the bike will start moving alot faster when the same touch is applied on it.

Neglecting gravity and other opposing forces
Thanks that makes sense.

I still dont think textbooks stating that a bus is not possible to be pushed by hand is a great way to illustrate inertia, they should just say it would accelerate less (if there was no friction).

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving