A block is pulled with constant tension up an incline, find the distance?

In summary, a 13kg mass is pulled along a frictionless horizontal floor for a distance of 5.1m before being pulled up an incline with an angle of 39 degrees and a coefficient of kinetic friction of 0.39. The mass is pulled by a tension of 68 N parallel to the incline. The final question is to find the distance traveled by the block up the incline before coming to rest, measured along the incline. The work-energy theorem can be used to solve this problem by equating the work done by tension to the change in mechanical energy (KE + PE). The given values for work done by tension, speed before traveling up the incline, work done by friction, and work
  • #1
clesling
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Homework Statement



A mass m = 13kg is pulled along a horizontal floor with no friction for a distance of d = 5.1m. Then the mass is pulled up an incline that makes an angle theta = 39 degrees with the horizontal and has a coefficient of kinetic friction u = 0.39. The entire time the massless rope is used to pull the block is pulled parallel to the incline at an angle of theta = 39 degrees (thus on the incline it is parallel to the surface) and has a tension of 68 N. How far up the incline does the block travel before coming to rest (measured along the incline)?


Homework Equations



I have answered the following questions and found these values to be correct.

The work done by tension before the block goes up the incline (on the horizontal surface) to be 269.5 Joules
The speed of the block right before it begins to travel up the incline is 6.4392 m/s
The work done by friction after a specific distance of x = 2.1 m up the incline (for x measured along the incline) is -81.171 Joules
The work done by gravity after the block has traveled a specific distance of x = 2.1m (for x measured along the incline) is -168.54 Joules


The Attempt at a Solution



I have attempted to incorporate the above ideas and answers into the solution, but have no idea if any of these answers are relevant to the final question which is to find the total distance traveled by the object up the incline.
 
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  • #2
hi clesling! :smile:
clesling said:
A mass m = 13kg is pulled along a horizontal floor with no friction for a distance of d = 5.1m. Then the mass is pulled up an incline that makes an angle theta = 39 degrees with the horizontal and has a coefficient of kinetic friction u = 0.39. The entire time the massless rope is used to pull the block is pulled parallel to the incline at an angle of theta = 39 degrees (thus on the incline it is parallel to the surface) and has a tension of 68 N. How far up the incline does the block travel before coming to rest (measured along the incline)?

I … have no idea if any of these answers are relevant to the final question which is to find the total distance traveled by the object up the incline.

yes, use the work-energy theorem …

work done = change in mechanical energy :wink:

(mechanical energy is KE + PE)
 

1. How do I calculate the distance a block is pulled up an incline?

In order to calculate the distance a block is pulled up an incline, you will need to know the constant tension applied, the mass of the block, the angle of the incline, and the coefficient of friction. You can then use the formula d = (mgh)/(Mgsinθ + μMgcosθ) to calculate the distance, where d is the distance, m is the mass of the block, g is the acceleration due to gravity, h is the height of the incline, θ is the angle of the incline, and μ is the coefficient of friction.

2. What is the significance of constant tension in this scenario?

Constant tension refers to the consistent force applied to the block as it is pulled up the incline. This constant tension allows us to use the formula mentioned above and accurately calculate the distance the block will travel.

3. How does the mass of the block affect the distance it is pulled up the incline?

The mass of the block affects the distance it is pulled up the incline because it is a factor in the formula used to calculate the distance. The greater the mass, the more force is needed to pull it up the incline, resulting in a shorter distance traveled.

4. Can you explain the role of the coefficient of friction in this scenario?

The coefficient of friction is a measure of how much resistance there is between two surfaces, in this case, the block and the incline. It affects the amount of force needed to pull the block up the incline, and therefore, it is included in the formula to calculate the distance.

5. Is the angle of the incline a significant factor in finding the distance the block is pulled?

Yes, the angle of the incline is a significant factor in finding the distance the block is pulled. This is because the angle affects the amount of force needed to pull the block up the incline, which is included in the formula for calculating the distance. A steeper incline will require more force and result in a shorter distance traveled.

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