Verify Solutions for Dynamics Problems Homework

In summary, a scenario is described where a car is driving up a steep hill while pulling a trailer. The maximum force the trailer hitch can withstand, as well as the mass of the car and trailer, are given. The question asks for the top speed the car could achieve after driving a certain distance up the hill. After drawing a free-body diagram and making some assumptions, the maximum velocity is calculated to be 36 m/s. However, another person suggests that the calculation may be incorrect due to the omission of gravity's component parallel to the slope.
  • #1
doug1
9
0

Homework Statement



You are driving home from the cottage and pulling a trailer behind your car. There is a steep hill with a 12 degree incline that you must drive up. You read the instructions for the trailer hitch which keeps the trailer attached to your car. The hitch can withstand a maximum force of 4.3 x 10^3 N. The car has a mass of 1.1 x 10^3 kg. The trailer has a total mass (including the stuff inside) of 2.7 x 10^2 kg. There is rolling friction between the trailer and road with μr = 0.15 (treat this just like kinetic friction). You start from the bottom of the hill at rest (a stop sign). What is the top speed you could achieve after driving 45.0 m up the hill?


The Attempt at a Solution



I drew a FBD of the trailer and then made the assumption that the maximum Ft (force of tension) pulling the trailer is 4.3 x 10^3 N. I then isolated variable 'a', and ascertained an acceleration of 14.5 m/s^2.

I then determined the maximum velocity to be 36 m/s. Can anyone verify this value?
 
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  • #2
Your procedure seems right. Hopefully you included all other forces such as the Normal and the Friction into your calculation.
 
  • #3
doug1 said:
ascertained an acceleration of 14.5 m/s^2.
I only get 12.45. Did you perhaps omit the component of gravity parallel to the slope?
 

1. How do I know if my solution is correct?

In order to verify the solution for a dynamics problem homework, you can follow these steps:

  • Step 1: Substitute the given values into the solution equations.
  • Step 2: Simplify the equations and solve for the unknown variables.
  • Step 3: Check if the solution satisfies all given conditions and equations.
  • Step 4: Double check your calculations and make sure there are no errors.

2. What should I do if my solution does not match the answer in the back of the textbook?

If your solution does not match the answer in the back of the textbook, it could be due to a few reasons:

  • There may be a mistake in your calculations.
  • The textbook may have a typo or error in the answer.
  • The problem may have multiple solutions and the textbook only shows one of them.

In order to determine the correct solution, it is best to check with your teacher or a classmate, or seek help from a tutor or online resource.

3. Can I use a calculator to verify my solutions?

Yes, you can use a calculator to verify your solutions for dynamics problems. However, it is important to note that calculators are not always accurate and may round numbers differently. It is always best to double check your calculations by hand to ensure accuracy.

4. What should I do if I get stuck on verifying a solution?

If you get stuck on verifying a solution, you can try the following:

  • Break the problem down into smaller parts and solve them separately.
  • Consult your textbook or class notes for similar examples and solutions.
  • Seek help from your teacher, a classmate, or a tutor.
  • Use online resources such as tutorials or forums for additional guidance.

5. How much time should I spend on verifying solutions for dynamics problems homework?

The amount of time you spend on verifying solutions for dynamics problems homework will vary depending on the complexity of the problem and your level of understanding. It is important to take your time and ensure accuracy, but also to not spend too much time on one problem. It is recommended to seek help if you are spending a significant amount of time on a single problem.

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