Sled pulled up incline at an angle with friction

In summary, the problem involves a child pulling a 3.6 kg sled at a constant velocity of 16 N along a slope that is 15 degrees to the horizontal. The sled moves at a constant velocity due to the equal forces of friction and the component of tension parallel to the slope. To find the acceleration of the sled when the rope is released, the coefficient of friction (\mu) is needed. Using the equation F=ma and f=\muN, the values for the forces and normal force (N) are calculated. However, there seems to be a discrepancy with the given answer and further clarification is needed.
  • #1
Strawer
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0

Homework Statement



A child pulls a 3.6 kg sled at 25 degrees to a slope that is 15 degrees to the horizontal, as in the figure. The sled moves at a constant velocity when the tension is 16 N. What is the acceleration of the sled if the rope is released?


Homework Equations



F=ma, f=[itex]\mu[/itex]N


The Attempt at a Solution



Constant velocity means that friction + the component from Fg shall equal FTx (tension component parallell to plane) that is FTx = f + Fx

Where FTx=cos(25)*FT=14.5 N and Fx=3.6*9.8=9.13 N

Now I want [itex]\mu[/itex] so that I can calculate f. And we know that N=cos(15)*mg+T*sin(25)=40.84 N

If we go back to the start, FTx=[itex]\mu[/itex]N+Fx so [itex]\mu[/itex]= [itex]\frac{ (FTx-Fx) }{N}[/itex]= [itex]\frac{14.5-9.13}{40.84}[/itex] = 0.131

When we release the sled N will reduce to N=mg*cos(15)=34.08 and so f=0.131*34.08=4.46 N

Fres=Fx-f=9.13-4.46=4.66 N

And the acceleration is a=[itex]\frac{F}{m}[/itex]=[itex]\frac{4.66}{3.6}[/itex]=1.3 m/s^2

But apparently this is not correct. Could someone please tell me what I've missed, this question has been very frustrating for me :(

Also, negative signs tend to mess upp my Latex, I apologize.
 
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  • #2
Here's the figure btw.
 

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  • #3
Anyone?
According to the answer sheet the correct answer should be 0.67 m/s^2 but I'm starting to wonder whether that's true or not?
 

1) What is the purpose of pulling a sled up an incline at an angle?

The purpose of pulling a sled up an incline at an angle is to demonstrate the effect of friction on objects moving on an inclined surface. This experiment allows scientists to observe and measure the amount of friction between the sled and the incline at different angles.

2) How does friction affect the movement of the sled on the incline?

Friction acts as a force that opposes the motion of the sled on the incline. As the angle of the incline increases, the force of friction also increases, making it more difficult to pull the sled up the incline.

3) What factors can affect the amount of friction between the sled and the incline?

The amount of friction between the sled and the incline can be affected by the weight of the sled, the material of the sled and the incline, and the roughness of their surfaces. The angle of the incline also plays a significant role in determining the amount of friction.

4) How can the amount of friction be measured in this experiment?

The amount of friction can be measured by attaching a spring scale to the sled and pulling it up the incline at different angles. The force measured by the spring scale will be equal to the force of friction acting on the sled. The angle at which the force of friction equals the weight of the sled is the angle of maximum friction.

5) What is the significance of this experiment in real-life scenarios?

This experiment helps scientists and engineers understand the effects of friction on objects moving on inclined surfaces. This knowledge can be applied in real-life scenarios such as designing vehicles that can travel up steep inclines, creating efficient conveyor belts, and improving the performance of sports equipment on different surfaces.

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