Forces of Motion: Solving Problems with Speed, Mass, and Acceleration

[AznBoi]

I need help with two more problems, thanks! I have work for one of the problems, please see if its close to being correct. Ty.

1. The driver of a speeding empty truck slams on the brakes and skids to a stop through distance d. a) If the truck carried a load that doubled its mass, what would be the truck's "skidding distance"? b) If the initial speed of the truck were halved, what would be the truck's "skidding distance"?

My work: a) If the truck carried a load that doubled its mass, the truck’s “skidding distance” would be half of the original distance in which the truck carried nothing.
b) If the initial speed of the truck were halved, the truck’s “skidding distance” would also be close to half of the original distance when the truck had 2 times more initial speed.


2. A truck loaded with sand acclerates along a highway. If the driving force on the truck remains constant, what happens to the truck's accerleration if its trailer leaks sand at a constant rate through a hole in its bottom?

I don't get how the sand would influence the acceleration of the truck if it is going down into a hole at the bottom. I mean the sand's inertia is accelerating forward but how would it affect going down the bottom?

 

[Doc Al]

1. The driver of a speeding empty truck slams on the brakes and skids to a stop through distance d. a) If the truck carried a load that doubled its mass, what would be the truck's "skidding distance"? b) If the initial speed of the truck were halved, what would be the truck's "skidding distance"?

My work: a) If the truck carried a load that doubled its mass, the truck’s “skidding distance” would be half of the original distance in which the truck carried nothing.
b) If the initial speed of the truck were halved, the truck’s “skidding distance” would also be close to half of the original distance when the truck had 2 times more initial speed.

You gave answers, but you didn't show how you got those answers. Hints: What force stops the truck? How does that force depend on the truck's mass? What acceleration does the force produce?

2. A truck loaded with sand acclerates along a highway. If the driving force on the truck remains constant, what happens to the truck's accerleration if its trailer leaks sand at a constant rate through a hole in its bottom?

I don't get how the sand would influence the acceleration of the truck if it is going down into a hole at the bottom. I mean the sand's inertia is accelerating forward but how would it affect going down the bottom?

Hint: The force remains constant, but does the mass?

 

[AznBoi]

You gave answers, but you didn't show how you got those answers. Hints: What force stops the truck? How does that force depend on the truck's mass? What acceleration does the force produce?


Hint: The force remains constant, but does the mass?

1) If the mass on the truck doubles, then its inertia would be less than before. Therefore it would be harder to stay in its original motion

If the initial speed were halved, then the distance would be half because the initial force is half?

2) ok, I get it I think. Because it's mass decreases as the force remains constant, its inertia increases, so does the acceleration of the truck?
Is it because the accerleration of an object is inversely proportional to its mass??

 

[AznBoi]

Am I on the right track?

 

[Doc Al]

1) If the mass on the truck doubles, then its inertia would be less than before. Therefore it would be harder to stay in its original motion

If the initial speed were halved, then the distance would be half because the initial force is half?

2) ok, I get it I think. Because it's mass decreases as the force remains constant, its inertia increases, so does the acceleration of the truck?
Is it because the accerleration of an object is inversely proportional to its mass??

Inertia is proportional to mass. But try to answer my earlier questions as precisely as possible.

 

[AznBoi]

You gave answers, but you didn't show how you got those answers. Hints: What force stops the truck? How does that force depend on the truck's mass? What acceleration does the force produce?


Hint: The force remains constant, but does the mass?

1. What force stops the truck:
The ground friction stops the truck.

How does that force depend of the truck's mass:
The more mass it has the smaller the inertia, so friction would stop it easier than if the mass was smaller, having more inertia (original line of motion)

What acceleration does the force produce:
F=ma?? so a= F/m ?

2. If sand falls below the truck at a constant rate, the driving force would increase proportionally. ?

Wait are the hints for two separate questions? lol

 

[Doc Al]

1. What force stops the truck:
The ground friction stops the truck.

Exactly: Kinetic friction stops the truck.

How does that force depend of the truck's mass:
The more mass it has the smaller the inertia, so friction would stop it easier than if the mass was smaller, having more inertia (original line of motion)

How does that friction force depend on the mass of the truck? (Stop using the word inertia. )

What acceleration does the force produce:
F=ma?? so a= F/m ?

How the force and mass changes determines how the acceleration changes. The acceleration (and speed) determines the stopping distance.

2. If sand falls below the truck at a constant rate, the driving force would increase proportionally. ?

You are told that the driving force remains constant. But a changing mass would affect the acceleration.

 

[AznBoi]

Oh I see it is because you need more acceleration when carrying a truck with more mass. So if you decrease the mass, the driving force would still remain constant, but the accleration would increase because there isn't that much weight right? Is that what you mean?

 

[AznBoi]

How does that friction force depend on the mass of the truck? (Stop using the word inertia. )

The more mass a truck has, the more friction force it takes. lol, this is just an intro homework to Newton's laws, I haven't really learned about kinetic friction yet.

 

[Doc Al]

Oh I see it is because you need more acceleration when carrying a truck with more mass. So if you decrease the mass, the driving force would still remain constant, but the accleration would increase because there isn't that much weight right? Is that what you mean?

If the force remains the same (which is given), the acceleration (given by a = F/m) will increase as the mass decreases.

 

[Doc Al]

The more mass a truck has, the more friction force it takes.

If the mass doubles, the friction force doubles. But what happens to the acceleration? (a = F/m)

 

[AznBoi]

I see, the acceleration decreases. Thanks for your help.