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--- 183_notes:examples:sledding [2014/10/13 05:15] – pwirving
+++ 183_notes:examples:sledding [2014/10/22 04:06] (current) – pwirving
@@ Line 1: / Line 1: @@
-===== Example: The Jumper =====
+===== Example: Sledding =====
 A little girl is riding her sled on a hill. If she starts a distance d up the hill, which makes an angle θ with the horizontal, how far will she travel along the flat snowy ground?
@@ Line 82: / Line 82: @@
 {{course_planning:projects:f2b.jpg?200|}}
-Need to find $f_{1} & f_{2}$
+Need to find $f_{1}$ & $f_{2}$
 To find $F_{1}$ we can say that the sum of the forces in the x direction are equal to $ma_{1}$ But we don't need this because we know that $f_{1}=μ_{k}N$.
-$\sum{F_{x}} = f_{1} - mgsinθ = ma_{1}
+$\sum{F_{x}} = f_{1} - mgsinθ = ma_{1}$
 The sum of the forces in the y direction we do need because this allows us to express N.
@@ Line 111: / Line 111: @@
 $$\Delta U_{g} = -(μ_{k}mgcosθ)d - (μ_{k}mg)x$$
+Substitute in the equation for gravitational potential energy for $\Delta U_{g}$
 $$+mg(y_f - y_i) = -μ_{k}mgdcosθ - μ_{k}mgx$$
+Rearrange to get the following expression.
 $$y_f - y_i = -μ_{k}(dcosθ + x)$$
-What is $y_f-y_i$ in terms of what we know?
+What is $y_f-y_i$ in terms of what we know? Eventually we want to express x in terms of variables we know.
 {{course_planning:course_notes:final_sledding.jpg?200|}}
+From the diagram of the incline we get:
 $$y_f-y_i =  -dsinθ$$
+Substitue $-dsinθ$ for $y_f-y_i$ and then rearrange to express x in terms of known variables.
 $$-dsinθ = -μ_{k}(dcosθ + x)$$
@@ Line 129: / Line 137: @@
 $$x = d (\dfrac{sinθ-μ_{k}cosθ}{μ_{k}})$$
+A check of the units reveals that:
 [x]=m
@@ Line 134: / Line 144: @@
 [d]=m
-All other quantities are unitless.
+Which makes sense as all the other quantities are unit less.
+$E = γmc^2$