Calculating Net Force on an Object Moving in a Plane

[crazy_shoes]

I'm having terrible difficulty starting this problem, it's one of the chapter excercises in the book and it's revisited in the homework later on. I'm going to give different data, as I would like to actually solve this one myself, I just need a kick start...

Homework Statement

We've got an object moving in a plane, no velocity is stated at all, just that it's moving. It's mass is 6.00 kg and it's coordinates are given by 2 equations, $$x = 4t^2 - 1$$ and $$y = 2t^3 + 6$$. They are asking what the net force acting on this object is at time t = 5.00s.

Homework Equations

I know somewhere in there I'm going to use kinematic equations. I started by trying to find $$\Delta X$$ and $$\Delta Y$$...



Thanks to anyone who can point me in the right direction!

 

[Avodyne]

It's in a plane, so position, velocity, acceleration, and force are all vectors with x and y components. The position vector is (x,y)=(4t²-1,2t³+6). Can you find the velocity vector? (How is velocity related to position?) Then, can you find the acceleration vector? Then, can you find the force vector?

 

[crazy_shoes]

Ah, that makes a lot of sense! Thank you so much! I was completely overlooking that.

 

[Avodyne]

Glad to help.

 

[crazy_shoes]

If I'm using position to get a velocity vector with the formula $$V_x_{avg} = \frac{\Delta x}{\Delta t}$$, can I use t = 0 for my $$t_i$$?

 

[Avodyne]

You should be computing instantaneous velocity, not average velocity.

I assume this is a calculus-based course?

 

[crazy_shoes]

For the formulas I have you still need $$\Delta x$$ and $$\Delta t$$

$$v_x = lim_{\Delta t \rightarrow 0}\frac{\Delta x}{\Delta t}$$

...and yes, this is calculus based.

I feel like I've missed a lesson or missed something in class.

 

[Avodyne]

That limit defines the derivative of x with respect to t. Given x as a simple function of t, say, x=t², can you compute the derivative dx/dt ?

 

[crazy_shoes]

OH! So it would be 2t then... If the function was in fact $$t^2$$.

 

[meopemuk]

I'm having terrible difficulty starting this problem, it's one of the chapter excercises in the book and it's revisited in the homework later on. I'm going to give different data, as I would like to actually solve this one myself, I just need a kick start...

Homework Statement

We've got an object moving in a plane, no velocity is stated at all, just that it's moving. It's mass is 6.00 kg and it's coordinates are given by 2 equations, $$x = 4t^2 - 1$$ and $$y = 2t^3 + 6$$. They are asking what the net force acting on this object is at time t = 5.00s.

Homework Equations

I know somewhere in there I'm going to use kinematic equations. I started by trying to find $$\Delta X$$ and $$\Delta Y$$...

You would need two formulas:

1. Newton's second law $\mathbf{F} = m \mathbf{a}$ and
2. definition of components of the acceleration vector

$$a_x = d^2x(t)/dt^2$$
$$a_y = d^2y(t)/dt^2$$

Eugene

 

[crazy_shoes]

So, if my position in the x direction is a function of time, like $$x=2t^2$$ the derivative of that is $$4t$$ which should be my velocity in the x direction. Then a second derivative should give me 4 and that should be my acceleration in the x direction. Am I on the right track?

 

[meopemuk]

So, if my position in the x direction is a function of time, like $$x=2t^2$$ the derivative of that is $$4t$$ which should be my velocity in the x direction. Then a second derivative should give me 4 and that should be my acceleration in the x direction. Am I on the right track?

Yes, you got it.

Eugene.

 

[crazy_shoes]

Thanks! It's much appreciated. Good thing I have a whole week to finish studying for my test!