Question

You and Tim, who is larger than you, are outside with a wagon. Tim (the bigger person) gets in the wagon and you (the smaller one) pull it. As you pull it, you accelerate until you reach a comfortable velocity. Then you stop and switch places with Tim. Tim now pulls you in the wagon, accelerating from a stop to a comfortable velocity. Now, Tim may be bigger than you, but you have been working out and are just as strong as Tim, so the force that Tim uses to pull the wagon is the same force that you used. You both pull with the exact same amount of force. Who was riding in the wagon when it had the greatest acceleration during start up? Why? Use Newton’s second law to explain.

Now Sara comes along, and she is the exact same size as you. However, she is even stronger than you! When she pulls you in the wagon, she pulls with a greater force than when you pull her. Now who is in the wagon when it has the greatest acceleration? Explain, using Newton’s second law.

Answer 1

Answer:

1. As both me and Tim  have the same amount of force and are able to pull the same weight with the same effect. However, Tim’s weight is greater than mine, so when I pull him it’s harder at the start as he is bigger and heavier than me.  If I was to be 35 kg and he was about ⅓ more my weight.

My power=Tims power

My weight<Tims weight    This creates a gap

So in conclusion , Tims speed at the start would be greater than mine asI weight less than him.

2. My power<Sara’s power

My weight=Sara’s weight          This creates a gap

This end up that Saras acceleration is greater than mine as she is even stronger than me.

Explanation:

Answer 2

I was riding in the wagon when it had the greatest acceleration during start up.

According to Newton's Second Law of Motion,

Force, F = $\frac{d}{dt} (mv)$ [m = mass of the object, v = velocity of the object]

F = m $\frac{dv}{dt}$ + v $\frac{dm}{dt}$

As the m is constant here, so the equation will be,

F = m $\frac{dv}{dt}$

or, F = m×a , a is the acceleration

Between Tom and I,

Now, if the Force applied is same,

a ∝ 1/m

As Tom is bigger than me, so in the first case, I was riding in the wagon when it had the greatest acceleration during start up.

In the second case,

The force is not same.

Sara applies more force than both of us and she is the exact same size as me.

If m is same, then,

F ∝ a

So, in the second case, Sara is in the wagon when it has the greatest acceleration.