Solve for the Maximum Incline | Car Acceleration & Power Problem

In summary, to find the steepest hill a 1100kg car can climb at 20 kph with constant engine power, we can use the equation F=ma to calculate the force of the car. Then, by finding the component of mg that matches the incline, we can use inverse trigonometry to find the angle of the steepest hill the car could climb.
  • #1
HT3
23
0

Homework Statement


A 1100kg car can accelerate from 0-60kph in 6.5 seconds. With constant engine power, what is the steepest hill the car could climb at 20 kph.


Homework Equations


F=ma
W=Fd
P=W/t
g=mgSin(theta)

maybe work energy theorem?

The Attempt at a Solution


Not Much...just conversions and I do not know where to go from here
60kph-->16.67m/s
a=16.67/6.5 = 2.56m/s^2

20km/h --> 5.56m/s
 
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  • #2
bump please help :(
 
  • #3
Okay so you need to think about the force of the car based on the mass and the acceleration. Draw yourself a diagram of an incline of steepness "S". Now put the car on it. You should have the force of the car moving up the incline and mg. You need to find the component of mg that matches the incline. Doing this, you can find a component that outweighs the force of the car moving forward. Hope that helps.
 
  • #4
ok so would it be mgsintheta? but i don't have theta? so how can i get the netforce acting on the car
 
  • #5
First find the force the car is exerting. What you want to do is insert that same force into your component of mg. You know the y component of mg by multiplication. So on the diagonal axis you will have a force equal and opposite to the car moving up the same axis, and then you will have mg on your y axis. Now you can use inverse trig to find the angle. Give that a try, I will be on for 20 more minutes before my next class.
 

1. What are the steps to solving a work problem?

The steps to solving a work problem may vary depending on the specific problem, but generally they include: identifying the problem, gathering and organizing relevant information, developing a plan or strategy, implementing the plan, and evaluating the solution.

2. How do I know which formula to use for a work problem?

The formula you use for a work problem will depend on the type of work being done. For example, if the problem involves force and distance, you may need to use the formula W = F x d. It's important to carefully read and understand the problem in order to determine the appropriate formula.

3. What are some common mistakes to avoid when solving work problems?

Some common mistakes to avoid when solving work problems include: not carefully reading and understanding the problem, using the wrong formula, miscalculating or misinterpreting units, and not checking your work for errors.

4. How can I check if my solution to a work problem is correct?

There are a few ways to check if your solution to a work problem is correct. One way is to use a different method to solve the problem and compare the results. You can also plug your solution back into the original problem to see if it satisfies all the given conditions. Lastly, if possible, you can ask someone else to check your work.

5. Can you give an example of a work problem and its solution?

Sure! Let's say you are trying to calculate the work done when lifting a 10 kg box to a height of 2 meters. Using the formula W = F x d, we can calculate the force needed to lift the box by dividing its weight (10 kg) by the acceleration due to gravity (9.8 m/s²). This gives us a force of approximately 1.02 Newtons. Then, we multiply the force by the height to get the work done, which in this case is 2.04 Joules.

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