What Went Wrong with my Kinetic Energy Problem?

In summary, the question asks about the change in kinetic energy when a force is applied at different angles to a moving toboggan on a frictionless surface. When the force is parallel to the ground, there is a 47% increase in kinetic energy, while at 38° above the horizontal, the increase is approximately 10%. The calculation for the second case does not need to involve mass or velocity.
  • #1
PiRsq
112
0
I don't know why I am getting a different answer but here is the question:


A toboggan is initially moving at a constant velocity along a snowy horizontal surface. Ignore friction. When a pulling force is applied parallel to the ground over a certain distance, the kinetic energy increases by 47%. By what percentage would the kinetic energy have changed if the pulling force had been at an angle of 38° above the horizontal?


A few things:

Ekf = Final kinetic energy
Eki = Initial kinetic energy
m=mass
vf=final velocity
vi=initial velocity
Now:

Case 1 (where the force applied is parallel to the ground)

2Facos0(mvf-mvi)=2(100 x 0.47)

mvf-mvi=(100 x 0.47)/Fa


Case 2 (where the force is at 38° to the horizontal)

2Facos38(mvf-mvi)=2(100 x y)

mvf-mvi= (100 x y )/FaCos38


Now equating the two equations:

100 x 0.47 = (100 x y)/cos38

Solving for y I got y=0.37

So the increase is ~ 10%, and the answer is 16%. What did I do wrong?
 
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  • #2
I'm not sure what you're calculating. Think of it this way:

(horizontal component of F)x (horizontal displacement) = KE(f)-KE(i)

The initial KE(i) is, of course, the same. The only difference in the two cases is the horizontal component of F. Try again.

Hint: No need for any formulas with m or v !
 
  • #3


First of all, it's great that you provided your calculations and showed your thought process. It's important to double check your work when solving problems like this, so let's take a closer look at your calculations.

In your first case, where the force is parallel to the ground, you correctly used the formula for work to determine the change in kinetic energy. However, in your second case where the force is at an angle of 38°, you used the same formula but with a different value for the work done (100 x y). This is where the error lies.

The work done in both cases should be the same, since the only difference is the angle of the force. So, in your second case, the work done should also be 100 x 0.47. This would give you a value of y=0.47, resulting in a 47% increase in kinetic energy.

Overall, your thought process was correct, but there was a small error in your calculations. Keep in mind to double check your work and make sure all the variables and formulas are consistent. Good luck with your future problem solving!
 

FAQ: What Went Wrong with my Kinetic Energy Problem?

What is kinetic energy?

Kinetic energy is the energy of motion. It is the energy an object possesses due to its motion, and is dependent on its mass and velocity.

How is kinetic energy calculated?

Kinetic energy is calculated using the formula KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.

What is the relationship between kinetic energy and velocity?

Kinetic energy is directly proportional to the square of an object's velocity. This means that as the velocity of an object increases, its kinetic energy increases exponentially.

Can kinetic energy be converted into other forms of energy?

Yes, kinetic energy can be converted into other forms of energy, such as potential energy or thermal energy. This conversion often occurs through collisions or friction.

How is kinetic energy important in everyday life?

Kinetic energy is important in everyday life as it is responsible for the movement and motion of objects. It is also a key concept in understanding the laws of motion and how forces affect objects in our daily lives.

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