Does the mass of an object affect its inertia?

[gazeem]

Homework Statement

Which of the following statements describes what must be true in the context of Newton’s First Law?

A) The tendency for drivers to keep moving linearly while the car makes a sharp turn on the road is an example of the concept of inertia.

B) An object with zero acceleration and an object traveling at a constant acceleration are considered similar states.

C) Mass is a measure of an object’s ability to resist motion or movement of any kind.

D) The object is difficult to bring to a complete stop due to its high initial speed.

Relevant Equations

F = ma

I know what the answer is supposed to be, but I don't understand why. Here is my logic as to why I thought a few of these suggestions should be the right answer.

"C) Mass is a measure of an object’s ability to resist motion or movement of any kind."

Considering F = ma, and that mass is basically the multiplier of how much force we'll need to apply to an object to get an acceleration of x, I would presume that mass *is* a measure of inertia, because the greater the mass, the more force you need to get an object to move at a particular acceleration.

(Is my logic in this true? Perhaps the reason this answer is incorrect is because this is more so related to Newton's Second Law)

"D) The object is difficult to bring to a complete stop due to its high initial speed."

If two bowling balls of the same mass (let's say 2kg) are rolling down a frictionless lane and Ball #1 is at a constant velocity of 5m/s and Ball #2 is at a constant velocity of 10m/s, and we want to stop the bowling bowls by blowing a big fan in the opposite direction the bowling balls will travel, the force needed to stop Ball #1 in one second would be:

F = 2kg * (-5m/s^2) = 10N in the opposite direction that the ball is traveling,

and the force needed to stop Ball #2 in one second would be :

F = 2kg*(-10m/s^2) = 20N in the opposite direction that the ball is traveling.

Therefore, the object with the higher initial speed did require more force to bring to a complete stop.

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The correct answer is "A" and I have no idea as to why.

 

[collinsmark]

Regarding C:

The key phrase here is "... of any kind." Moving at a constant velocity is one "kind" of movement. Does an object's mass cause it to resist moving at a constant velocity (in the absence of any external forces)?

Regarding D:

I agree that if you compare apples to apples (or bowling balls to bowling balls), you might have a point here. On the other hand, I don't think the statement in part D was necessarily about an apples to apples comparison. For example, compare a fast moving ping-pong ball with a moderately moving bowling ball.

Regarding A

If you don't know why that's true, you should think about it longer.
[Edit: a free body diagram might help. What are the forces on the person in the car, if any? If the car turns underneath the driver, what happens to the driver in absence of any forces?]

 

[Orodruin]

Just to add: Note that the question specifically refers to Newton’s first law. F=ma relates to Newton’s second law.

 

[CWatters]

Some answers _may_ be true in certain situations but the question asks "Which of the following statements describes what _must_ be true".

So for example high speed alone doesn't make something hard to stop. Consider photons which travel at errr the speed of light.

 

[gazeem]

Regarding C:

The key phrase here is "... of any kind." Moving at a constant velocity is one "kind" of movement. Does an object's mass cause it to resist moving at a constant velocity (in the absence of any external forces)?

Regarding D:

I agree that if you compare apples to apples (or bowling balls to bowling balls), you might have a point here. On the other hand, I don't think the statement in part D was necessarily about an apples to apples comparison. For example, compare a fast moving ping-pong ball with a moderately moving bowling ball.

Regarding A

If you don't know why that's true, you should think about it longer.
[Edit: a free body diagram might help. What are the forces on the person in the car, if any? If the car turns underneath the driver, what happens to the driver in absence of any forces?]

After thinking about A some more, I think I have a better understanding: If a car is turning, the force that is acting on the car to make it turn is not acting on the driver. Considering the force is, let's pretend 100N on the car, that would cause a reasonable amount of change in direction in the car because the car is heavy, but if that force were acting on the driver it would smash them into the side of the car. Within the frame of reference (the car), there are no forces that are acting on the driver besides gravity and normal force, so much like how the rotation of the Earth does not change my direction when I'm walking, the driver is sill in a linear direction when the car turns, as weird as that is to think about.

 

[PeroK]

After thinking about A some more, I think I have a better understanding: If a car is turning, the force that is acting on the car to make it turn is not acting on the driver. Considering the force is, let's pretend 100N on the car, that would cause a reasonable amount of change in direction in the car because the car is heavy, but if that force were acting on the driver it would smash them into the side of the car. Within the frame of reference (the car), there are no forces that are acting on the driver besides gravity and normal force, so much like how the rotation of the Earth does not change my direction when I'm walking, the driver is sill in a linear direction when the car turns, as weird as that is to think about.

This dosn't make sense to me. The only part of a car that is in contact with the road is the tyres. All the force to make a turn must come from the contact between the tyres and the road. This force is transmitted though the entire vehicle. In fact, if you think about it, the force is ultimately transmitted from one atom/molecule to the next.

Some of the force is transmitted to the driver through his/her contact points with the car: seat, seat-belt, steering wheel or car door in case of a sharp turn.

In any case, when a car is turning the driver is subjected to a centripetal force towards the centre of the turning circle. This force prevents the driver continuing in a straight line.

Eventually, just the right amount of force is applied to every component or occupant of the car to achieve a uniform acceleration. You might like to think about why this is.

If you start thinking about the rotation of the Earth, then you must ask yourself what you mean by a straight line? Also in this context there is the Coriolis Force/Effect:

https://en.wikipedia.org/wiki/Coriolis_force

 

[CWatters]

After thinking about A some more, I think I have a better understanding: If a car is turning, the force that is acting on the car to make it turn is not acting on the driver. Considering the force is, let's pretend 100N on the car, that would cause a reasonable amount of change in direction in the car because the car is heavy, but if that force were acting on the driver it would smash them into the side of the car. Within the frame of reference (the car), there are no forces that are acting on the driver besides gravity and normal force,

That's wrong. If a car goes around a curved path the driver must as well (unless he falls out!). So there must be a force acting on the driver. I suspect the answer they want is "friction between the driver and the seat".

so much like how the rotation of the Earth does not change my direction when I'm walking

Not sure what you are trying to say but the rotation of the Earth certainly does "change your direction", both as it rotates and as it orbits the sun.

[/Quote]the driver is sill in a linear direction when the car turns, as weird as that is to think about.
[/QUOTE]

No, consider a car on an oval race track. On one straight the car and driver might be heading and facing north, on the other they might be heading and facing south. They both rotate 360 degrees every lap.