Question

On an essentially frictionless, horizontal ice rink, a skater moving at 3.9 m/s encounters a rough patch that reduces her speed to 48% of her original speed due to a friction force that is 24% of her weight. Use the work—energy theorem to find the length of this rough patch.

Answer 1

d = 2.5 m

Step-by-step explanation:

• The work-energy theorem, states that the change in the kinetic energy of a body, is equal to the work done on the object, by the net external force on it, as follows:

`\Delta K = W_(net) =- (F_(net) * d_(rp)) (1)`

`\Delta K = K_(f) - K_(0) = (1)/(2) * m * (v_(f) ^(2) - v_(0) ^(2) ) (2)`

• In this case, our givens are as follows:
• v₀ = 3.9 m/s vf = 0.48*3.9 m/s = 1.87 m/s Fnet = 0.24*m*9.8 m/s2.
• Replacing by the givens in (1) and (2), rearranging and simplifying common terms, we can solve for drp, as follows:

`v_(f)^(2) -v_(0)^(2) = - 0.24*g* d_(rp) \\ \\ (1.87m/s)^(2) -(3.9m/s)^(2) = -0.24*9.8m/s2*d_(rp)`

`d_(rp) =(-11.7(m/s)2)/(-2*0.24*9.8 m/s2) = 2.5 m`