# math

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Three forces act on a hockey pick as it slides across the ice; the normal force N represents the force the ice exerts upward on the puck and is given by N= <0,0,100>, the gravitational force G represents the downward force of gravity on the puck and is given by G = <0,0,-100>, and the force due to friction F has a magnitude |F|=μ|N| and is in the direction opposite of whatever direction the puck is traveling, where μ is the coefficient of kinetic friction. Work (W) is done by any force A is given by W = A.s where s is the displacement vector associate with an object's motion. If an object moves away from (x1,y1,z1) to (x2,y2,z2), it's displacement can be represented by s = (x2-x1) xhat + (y2-y1) yhat = (z2-z1) zhat.
Consider a puck that moves from (1,1,0) to (3,3,0) on very slippery ice with a coefficient of kinetic friction of .15 and answer the following questions:
a. WHat is the displacement s of the puck? Write your answer in both component form and magnitude/direction.
b. What is the force of friction F acting on the puck? Write your answer in component form rounding to 1 decimal place.
c. How much work does friction do on the puck?
d. How much work does gravity do on the puck?
e. How much work does the normal force do on the puck?