Time remaining:
need answers to a 2 part question

Physics
Tutor: None Selected Time limit: 0 Hours

Consider a skier heading down a 9.5° slope. Assume the coefficient of friction for waxed wood on wet snow is μk=0.10 and use a coordinate system in which down the slope is positive.

θ = 9.5 °

Calculate the acceleration of the skier in m/s2.

Find the angle of the slope down which this skier could coast at a constant velocity in degrees.

Jul 16th, 2014

Answers: 0.65 m/s2; 5.7°.

Choose the coordinate system with x-axis directed to the right and the y-axis directed downwards.

The gravity force acting of the skier is W = (0, mg). It can be decomposed into the sum of two forces, FN which is perpendicular to the slope and FT directed along the slope. Their magnitudes are

FN = mg cos θ and FT = mg sin θ, where θ = 9.5°.

The remaining forces acting on the skier are the reaction force -FN and the friction force Fk which is directed along the slope but opposite to the force FT. The magnitude of the friction force is

Fk = μk FN = μk mg cos θ. The resultant of all forces has the magnitude F = FT – Fk =

mg(sin θ – μkcos θ) and creates the acceleration a = F/m = g(sin θ – μkcos θ) =

9.81 (sin 9.5° - 0.10 * cos 9.5°) = 0.65 m/s2.

To answer the second question we need to solve an equation a = 0.

Then sin θ – μkcos θ = 0, tan θ = μk, and θ = tan–1 μk = tan–1 0.10 = 5.7°.



Mar 18th, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Jul 16th, 2014
...
Jul 16th, 2014
Feb 21st, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer