How Does Increasing Pulling Force Affect the Average Velocity of a Trolley?

[Ayoub99k]

Homework Statement

Investigate the effect of the pulling force on average velocity. You will be given a trolley and a ramp and slotted masses to create pulling force.

Homework Equations

F=ma
Average velocity = d/t

The Attempt at a Solution

My hypothesis is that as we increase the pulling force by using slotted masses, the average velocity of the trolley will be increased. I think that for this experiment we can use the formula F=ma. Where we can use a as average velocity although it acceleration. Since there is no other formula we can use apart from this. I think the question is referring to acceleration by mentioning average velocity. I am going to add weights to make a pulling force and as i push the trolley down the ramp with different force, this will cause the average velocity to increase.

Only thing i want to clarify about my above answer is. Am i right about we can say that average velocity is same as acceleration for this experiment?

 

[berkeman]

Homework Statement

Investigate the effect of the pulling force on average velocity. You will be given a trolley and a ramp and slotted masses to create pulling force.

Homework Equations

F=ma
Average velocity = d/t

The Attempt at a Solution

My hypothesis is that as we increase the pulling force by using slotted masses, the average velocity of the trolley will be increased. I think that for this experiment we can use the formula F=ma. Where we can use a as average velocity although it acceleration. Since there is no other formula we can use apart from this. I think the question is referring to acceleration by mentioning average velocity. I am going to add weights to make a pulling force and as i push the trolley down the ramp with different force, this will cause the average velocity to increase.

Only thing i want to clarify about my above answer is. Am i right about we can say that average velocity is same as acceleration for this experiment?

Welcome to the PF.

No, in general average velocity will not be the same as acceleration. Is there friction involved in this experiment? How hefty are the wheels of the trolley?

I'd recommend against using "a" for both the acceleration and "average" velocity. Use Va or something similar for average velocity.

Do you know the equations of motion for constant acceleration (gravity for example)? There is one for the distance as a function of time, and another for velocity as a function of time...

 

[Ayoub99k]

There will not be any friction. Also are you suggesting for this experiment they want us to use the formula f=ma. So they are saying take average velocity as acceleration?
Equation for constant velocity is v = u + at i think.

But which formula do you think they want us to use? f=ma or not? As they want us to investigate effect of force and average velocity. but as i said the formula f=ma doesn't have average velocity. but its the only formula that uses force and acceleration. Get my question?

 

[berkeman]

There will not be any friction. Also are you suggesting for this experiment they want us to use the formula f=ma. So they are saying take average velocity as acceleration?
Equation for constant velocity is v = u + at i think.

But which formula do you think they want us to use? f=ma or not? As they want us to investigate effect of force and average velocity. but as i said the formula f=ma doesn't have average velocity. but its the only formula that uses force and acceleration. Get my question?

F=ma tells you that the acceleration is proportional to the force applied. As you add more weight, there will be more force applied in the direction of the acceleration. But there will also be more mass to be accelerated, so you need to work out the equation for the motion of your trolley on the ramp as a function of the mass applied...

And yes, the equation I was thinking of for velocity is $$v(t) = v(0) + a * t$$

You would substitute a = F/m into that equation to see how the velocity is affected by adding more weights...

 

[Ayoub99k]

Got it :) But would there be any issue if i used f=ma for average velocity as the question states? As i am preparing this for a younger class.

 

[berkeman]

Got it :) But would there be any issue if i used f=ma for average velocity as the question states? As i am preparing this for a younger class.

So you will be the instructor for this lab? In any case, I don't think you should be confusing the concepts of acceleration and average velocity. As you initially stated, the Vave is the total distance traveled divided by the total transit time. The transit time depends on the acceleration, because a higher acceleration will give a higher velocity profile for the transit. The way you show that the transit times are equal for the different masses (assuming no friction effects) is by showing that a=F/m from the initial relevant equation that you listed.

 

[Ayoub99k]

Oh not at all. Its just i am carrying this experiment for my students aged 14. And their syllabus mentions only the formula F=ma which i gave you but is asking for average velocity in the question. So I'm saying just to make it simpler for them, can i just take average velocity as the same as acceleration

 

[berkeman]

Oh not at all. Its just i am carrying this experiment for my students aged 14. And their syllabus mentions only the formula F=ma which i gave you but is asking for average velocity in the question. So I'm saying just to make it simpler for them, can i just take average velocity as the same as acceleration

No. For one thing they have different units. Acceleration has units of m/s^2 and velocity has units of m/s. Are no other equations given in this lesson?

 

[Ayoub99k]

No. The issue I am facing is the task i have isn't giving much detail making the task confusing.

Plan an investigation to test how the size of the pulling force affects the average velocity of the trolley of the toy car

 

[berkeman]

Plan an investigation to test how the size of the pulling force affects the average velocity of the trolley of the toy car

Well adding weight to the trolley is different from pulling it with a stronger force, right? If you add force by adding weight, as we've seen, the acceleration stays the same because of a=F/m.

To see that adding more pulling force increases the acceleration, you need to add more pulling force and not add mass to the trolley. You could use a string and pulley on the edge of a tabletop, for example, to pull the trolley with various forces via weights on the end of the string hanging off the table...

 

[Ayoub99k]

If i use a ramp, a pulley, weights to create the pulling force. Can i use the formula f=ma for average velocity then?

 

[berkeman]

If i use a ramp, a pulley, weights to create the pulling force. Can i use the formula f=ma for average velocity then?

Not that I can see. Can you post a sketch of your setup, the free body diagram (FBD) of the trolley and the math that justifies doing so?

 

[Ayoub99k]

The set up:

We want to test the relationship of force and average velocity

 

[haruspex]

The set up:

We want to test the relationship of force and average velocity

There is a fundamental problem with that: there is no specific relationship. It will depend on what is held constant.
If you run each test over the same distance but vary the weight, the average velocity will be found to vary as the square root of the weight; if instead you compare how far it travels in a fixed time as the weight changes, the average velocity will be directly proportional to the weight.