Calculating Max Uphill Acceleration for Skier on 5° Slope

[dazza555]

Homework Statement

A skier is going up a slope of 5 degrees to the horizontal. She is skating so only her skis provide propoltion. The static and kenetic friction coefficients for this situation are $$\mu$$$$_{s}$$=0.12 and $$\mu$$$$_{k}$$=0.07

Find the magnitude of her maximum possible uphill acceleration.

Homework Equations

Net force in the y direction is: Normal force - mg cos 5 deg =0
Therefore Normal force = mg cos 5 deg

Max acceleration: F in x /m = a = -mg sin 5 deg + max static friction/m

The Attempt at a Solution

I then put all my numbers in like so:
Max acceleration= -mg*sin 5 deg + 0.12 (mg*cos 5 deg)/m
the m cancels and using 9.8 for g I got

0.32ms$$^{-2}$$

 

[mark726]

I would approach this problem by first understanding the physical principles involved. In this case, the skier is moving up a slope, which means that gravity is acting against her motion. The skier is also using her skis to provide propulsion, which means that there is a force acting in the direction of motion.

I would then identify the relevant equations and variables, which in this case are the net force in the y direction, the normal force, and the maximum acceleration. Using the given information, I would calculate the normal force by using the equation Normal force = mg cos 5 deg. I would then use the equation for maximum acceleration, which is a = -mg sin 5 deg + max static friction/m. Plugging in the values, I would solve for the maximum acceleration to be 0.32 ms^-2.

Next, I would check my answer for reasonableness. Is the magnitude of the maximum acceleration reasonable for a skier on a 5 degree slope? Does it make sense based on the given coefficients of friction? I would also consider any potential sources of error or assumptions made in my calculations.

Finally, I would communicate my solution clearly and concisely, including any relevant diagrams or calculations. I would also discuss any limitations or potential areas for further research or investigation.