Gr. 12 Energy Problem - Pulling a Wagon

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In summary, the conversation discusses a problem involving a parent pulling a wagon with a combined mass of 50kg and doing 2.2 x 10^3 J of work over a distance of 60m at a constant speed. The coefficient of friction for the surfaces in contact is 0.26. The conversation also includes a solution attempt and a discussion about significant digits and accuracy. The final solution involves calculating the magnitude of the force applied by the parent and the angle at which the force is applied. It is recommended to use three digits in the calculations and determine the angle from the ratio of the vertical and horizontal components.
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Deceit
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Homework Statement



This is from a book for a correspondence course I'm taking. I don't have access to teachers, so hopefully some of you can fill that role :)

A parent is pulling a wagon. The child and the wagon have a combined mass of 50kg and the adult does 2.2 x 10^3 J of work pulling the two 60m at a constant speed. The coefficient of friction for the surfaces in contact is 0.26.

a) Determine the magnitude of the force applied by the parent.
b) Determine the angle at which the parent is applying this force.


Homework Equations



W = F * d
F(k) = u(k) * F(N)


The Attempt at a Solution



For the horizontal component of F(A):
W = F * d
2.2 x 10^3 J = F(Ah) * (60m)
F(Ah) = 37 N

To find the vertical component of F(A):
F(v) = F(N) + F(g) + F(Av)
(v means vertical)

F(N) = F(k) / u(k)
and, because the horizontal forces balance, F(Ah) = F(k)
Because the forces are balanced, F(v) = 0 so:

0 = (F(f) / u(f)) + (m * g) + F(Av)
-F(Av) = (37N / 0.26) + (50kg)(-9.8N/kg)
-F(Av) = -350N
F(Av) = 350N

Plugging in the component forces into the pythagorean theorem, I find F(A) = 350N
I'm only using two sig digs because they only use one in the question, and the book instructs to use one more sig dig during intermediate calculations than the original question uses. So, for the final answer, F(A) should actually be 400N to one sig dig.

As for the angle, using trig I find it to be 90 degrees.

Now, this angle is very steep (obviously), which is leading me to believe I did something wrong. Does this solution make sense or am I thinking about this the wrong way? Any insight is appreciated!
 
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  • #2
Be careful with the significant digits. It is better to use more than required than to loose accuracy. The instructions says that you have to use one digit more than the number of significant digits in the original data. That is two in this problem so do the calculations with 3 digits, and round off to two at the end.

You calculated the total applied force with two digits, which happened to be the same as the vertical component with that accuracy. You lost one digit and got the angle with one significant digit: 90 degree, which is not a sensible answer. And it was unnecessary to calculate the magnitude of the applied force. Calculate the angle from the tangent: you get 84 degrees. That is acceptable, is not it?

ehild
 
  • #3
ehild said:
Be careful with the significant digits. It is better to use more than required than to loose accuracy. The instructions says that you have to use one digit more than the number of significant digits in the original data. That is two in this problem so do the calculations with 3 digits, and round off to two at the end.

You calculated the total applied force with two digits, which happened to be the same as the vertical component with that accuracy. You lost one digit and got the angle with one significant digit: 90 degree, which is not a sensible answer. And it was unnecessary to calculate the magnitude of the applied force. Calculate the angle from the tangent: you get 84 degrees. That is acceptable, is not it?

ehild

The first part of the question did ask for the magnitude of the applied force. As for the significant digits, the question gave values of 50kg and 60m, each of which would technically only have one significant digit, no?

Thanks for the reply
 
  • #4
The other data clearly have 2 significant digits. 0 can be a significant digit, why not? So 50kg and 60 m have also two significant digits. If they wanted to use only one significant digit, they would have written them as 5 x 10^1 and 6 x 10^1.

If you see that the value of length, for example is 300000 m, it is given with 6 significant digits. The same would be 3.0x10^5 m with two significant digits.

OK, the magnitude of the force was also asked. But use three digits in the calculation. And determine the angle from the ratio of the vertical and horizontal components. ehild
 
  • #5
ehild said:
The other data clearly have 2 significant digits. 0 can be a significant digit, why not? So 50kg and 60 m have also two significant digits. If they wanted to use only one significant digit, they would have written them as 5 x 10^1 and 6 x 10^1.

If you see that the value of length, for example is 300000 m, it is given with 6 significant digits. The same would be 3.0x10^5 m with two significant digits.

OK, the magnitude of the force was also asked. But use three digits in the calculation. And determine the angle from the ratio of the vertical and horizontal components.


ehild

According to the book, any trailing zeros without a decimal place are not considered significant. But, I guess it really doesn't make sense to only use one sig dig in this case, so I'll consider the zeros significant.

Thanks for the help
 

Related to Gr. 12 Energy Problem - Pulling a Wagon

1. What is the Gr. 12 Energy Problem about?

The Gr. 12 Energy Problem is a physics problem that involves calculating the amount of work and energy required to pull a wagon a certain distance.

2. How do I approach solving the Gr. 12 Energy Problem?

First, you need to identify the given information, such as the mass of the wagon, the distance it needs to be pulled, and any other relevant data. Then, you can use the equations for work and energy to calculate the required values.

3. What are the key equations needed to solve the Gr. 12 Energy Problem?

The key equations are:
- Work (W) = Force (F) x Distance (d)
- Kinetic Energy (KE) = 1/2 x Mass (m) x Velocity (v)^2
- Gravitational Potential Energy (PE) = Mass (m) x Gravity (g) x Height (h)

4. Are there any important assumptions to consider when solving the Gr. 12 Energy Problem?

Yes, there are a few assumptions that need to be considered:
- The wagon is being pulled on a flat, frictionless surface.
- The force applied to the wagon is constant.
- The wagon starts from rest and ends at rest.
- All energy is conserved and there is no external energy input or output.

5. How can I check if my solution to the Gr. 12 Energy Problem is correct?

You can check your solution by making sure it follows the law of conservation of energy. This means that the total energy before pulling the wagon should be equal to the total energy after pulling the wagon. Additionally, you can also plug your calculated values back into the original equations to make sure they match.

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