How Does Mass Affect the Time It Takes Objects to Slide Down an Inclined Plane?

[x86]

Homework Statement

If the incline plane is 10 m long, and it is elevated at an angle of 30 degrees: If a 5kg object takes t1 seconds to go down the ramp and a 10kg object takes t2 seconds to go down the ramp... What is the relationship between t1 and t2?

Homework Equations

F = ma
Fx of slope = mgsinx
Fnorm = mgcosx

The Attempt at a Solution

If the incline plane is 10 m long, and it is elevated at an angle of 30 degrees... Then this means the x component of acceleration down the ramp is 4.9 m/s^2 meaning that a 5 kg object and 20 kg object will take the same amount of time to go down this 10 m ramp.

This is correct, right?

Secondly:

Also, if you throw an object up, when Vf = 0 it will start accelerating downwards.

Does this mean the velocity increases, or decreases? I answered in class that it depends on relativity, being as its a vector quantity (i.e. up can be negative or down can be negative). The teacher said this is wrong, and the velocity has to increase. Why?

 

[Sourabh N]

Homework Statement

If the incline plane is 10 m long, and it is elevated at an angle of 30 degrees: If a 5kg object takes t1 seconds to go down the ramp and a 10kg object takes t2 seconds to go down the ramp... What is the relationship between t1 and t2?

Homework Equations

F = ma
Fx of slope = mgsinx
Fnorm = mgcosx

The Attempt at a Solution

If the incline plane is 10 m long, and it is elevated at an angle of 30 degrees... Then this means the x component of acceleration down the ramp is 4.9 m/s^2 meaning that a 5 kg object and 20 kg object will take the same amount of time to go down this 10 m ramp.

This is correct, right?

Yes, that is correct.

Secondly:

Also, if you throw an object up, when Vf = 0 it will start accelerating downwards.

Does this mean the velocity increases, or decreases? I answered in class that it depends on relativity, being as its a vector quantity (i.e. up can be negative or down can be negative). The teacher said this is wrong, and the velocity has to increase. Why?

It's possible that your teacher was thinking about the magnitude of the velocity (also known as speed) which does increase as the object starts falling downwards.

 

[x86]

Yes, that is correct.
It's possible that your teacher was thinking about the magnitude of the velocity (also known as speed) which does increase as the object starts falling downwards.

Thank you.

Also, it does increase if it falls downwards. But, what if you make downwards negative and upwards positive?

Then say it will go from 0 to -10m/s to -20m/s etc. Would this be considered decreasing?

Or is the magnitude of the quantity the absolute value of it?

magnitude velocity = |V|

Magnitude is the absolute value, so, yes, it will always be increasing.

If your answer was "it depends on relativity, being as its a vector quantity (i.e. up can be negative or down can be negative)", it's absolutely right.
But if instead your answer was "it depends on relativity, being as its a vector quantity", he might have ruled it out because it's incomplete.

Ah okay, thank you

 

[Sourabh N]

Magnitude is the absolute value, so, yes, it will always be increasing.

If your answer was "it depends on relativity, being as its a vector quantity (i.e. up can be negative or down can be negative)", it's absolutely right.
But if instead your answer was "it depends on relativity, being as its a vector quantity", he might have ruled it out because it's incomplete.

 

[Nickie]

I would like to provide a response to these statements and questions. Firstly, yes, your understanding of the relationship between t1 and t2 is correct. Since both objects have the same x component of acceleration down the ramp, they will take the same amount of time to travel the same distance. This is due to the fact that the only force acting on the objects is the force of gravity, which is constant for both objects.

As for the second question, the velocity does indeed increase as the object travels upwards and then decreases as it falls back down. This is because velocity is a vector quantity, meaning it has both magnitude and direction. When the object is thrown upwards, it has a positive velocity and as it reaches its highest point, the velocity becomes zero. However, as it falls back down, the velocity becomes negative, indicating a change in direction. So, the velocity does increase in the upwards direction and then decreases in the downwards direction. It is important to consider the direction of the velocity when discussing its change.