Finding net force from position vector

[CassLovesKinematics]

Homework Statement

A helicopter (weight 2.48*10^5 N) has a given position of r = (0.042 m/s^3)t^3*i + (1.9 m/s)t*j - (0.098 m/s^2) t^2 k.
Find the net force of the helicopter at t = 9.5 , express the components of the net force in newtons.

Relevant Equations

1 N = 1kg*m/s^2
F = m*a

I understand that you have to take second derivative of r to find a
Doing it in dr^2/dt^2 = 6(0.042 m/s^3) t*i - 0.196 m/s^2 k, and then multiply (2.48*10^5) to 6(0.042*9.5) and to -0.196

However, my homework platform is NOT accepting 593712 N (or any rounding of it)for i vector and -48608 (or any rounding of it) for k
It INSTEAD insists that the correct answer for i is 6.1*10^4 and K is -5*10^3. Both of these answers are both a whole magnitude off, and that math is wrong. I read that pearson can sometimes get it wrong, but I thought that was years ago. Am I doing something wrong here, I've run it countless times.

 

[jg21]

Keep in mind, the weight given is in [Newtons]. Which is defined as Weight = mass * g. Perhaps you should find the mass of the helicopter, by dividing Weight/g. Then multiply this mass by your acceleration at t = 9.5 (which looks correct to me). ultimately, you'll see that your ##'s are just a factor of 9.81 too high.

 

[CassLovesKinematics]

Keep in mind, the weight given is in [Newtons]. Which is defined as Weight = mass * g. Perhaps you should find the mass of the helicopter, by dividing Weight/g. Then multiply this mass by your acceleration at t = 9.5 (which looks correct to me). ultimately, you'll see that your ##'s are just a factor of 9.81 too high.

wow this was so helpful. It makes so much sense now.

 

[kuruman]

Numerical problems like this are easier to troubleshoot if you (a) express and solve the problem in symbolic form first, then (b) substitute numbers. Here you have
(a)
$\mathbf r=at^3~\mathbf{\hat i}+bt~\mathbf{\hat j}+ct^2~\mathbf{\hat k}$
$\dfrac{d^2 \mathbf r}{dt^2}=6at~\mathbf{\hat i}+0~\mathbf{\hat j}+2c~\mathbf{\hat k}$
$\mathbf{F}_{\text{Net}}=\dfrac{W}{g}\left(6at~\mathbf{\hat i}+2c~\mathbf{\hat k}\right)$
(b)
Lay out a table with the given numbers with units, preferably on a spreadsheet.
Lay out a second table with all the calculated quantities according to the symbolic form you have derived.
If the answer does not look right, you can examine each cell individually and figure out where the problem lies.

For example, if you find that you entered a wrong "Given" parameter, when you enter the right number, the spreadsheet will automatically recalculate the answer. If the input parameters are all correct but not the answer, then there must be something wrong with one of the cells in the "Calculated" table. A spreadsheet beats a calculator 100% of the time as far as pinpointing errors is concerned.

Here is a screenshot of my spreadsheet calculation for this problem based on the formulas shown above in step (a).

 

[CassLovesKinematics]

Keep in mind, the weight given is in [Newtons]. Which is defined as Weight = mass * g. Perhaps you should find the mass of the helicopter, by dividing Weight/g. Then multiply this mass by your acceleration at t = 9.5 (which looks correct to me). ultimately, you'll see that your ##'s are just a factor of 9.81 too high.

Gah me and my study buddy were so stumpe

Numerical problems like this are easier to troubleshoot if you (a) express and solve the problem in symbolic form first, then (b) substitute numbers. Here you have
(a)
$\mathbf r=at^3~\mathbf{\hat i}+bt~\mathbf{\hat j}+ct^2~\mathbf{\hat k}$
$\dfrac{d^2 \mathbf r}{dt^2}=6at~\mathbf{\hat i}+0~\mathbf{\hat j}+2c~\mathbf{\hat k}$
$\mathbf{F}_{\text{Net}}=\dfrac{W}{g}\left(6at~\mathbf{\hat i}+2c~\mathbf{\hat k}\right)$
(b)
Lay out a table with the given numbers with units, preferably on a spreadsheet.
Lay out a second table with all the calculated quantities according to the symbolic form you have derived.
If the answer does not look right, you can examine each cell individually and figure out where the problem lies.

For example, if you find that you entered a wrong "Given" parameter, when you enter the right number, the spreadsheet will automatically recalculate the answer. If the input parameters are all correct but not the answer, then there must be something wrong with one of the cells in the "Calculated" table. A spreadsheet beats a calculator 100% of the time as far as pinpointing errors is concerned.

Here is a screenshot of my spreadsheet calculation for this problem based on the formulas shown above in step (a).

View attachment 374572

Holy formatting, you are a physicsforums.com GOAT