Question

Learning Goal: To practice Problem-SolvingStrategy 7.3 Conservation of energy with nonconservativeforces.

While a roofer is working on a roof that slants at = 36.0 above the horizontal,heaccidentally nudges his = 8.50 toolbox, causing it to start sliding downward,starting from rest. Africtional force of magnitude $f_k$ = 22.0 acts on the toolbox as it slides. If the boxstarts = 4.25 from the lower edge of the roof, how fast will the toolbox be moving just as itreaches the edge of the roof? Assume thatthe acceleration due togravity is = 9.80 $m/s^2$ .

Problem Solving Strategy7.3 Conservation of energy withnonconservative forces

1. Identify the system youwill analyze, and decide on the initial and final states (positionsand velocities) you will use in solving the problem. Drawone ormore sketches showing the initial and finalstates.
2. Define your coordinatesystem, particularly the zero points for gravitational and elasticpotential energies (the point at which $y=0$ ).
3. List the initial andfinal kinetic and potential energies ( $K_i$ , $K_f$ , $U_i$ , and $U_f$ ) and identify any nonconservative forces.Write anexpression for the work, $W_other$ , done bythenonconservative forces.

4. Use the generalexpression

   

   for conservation of energyand solve to find the unknown quantity.

5. Does your answer makesense? Did friction slow the object down? Did any pushing forcesspeed the object up? Can you explain any negativesigns?

SET UPBefore writing any equations, organizeyour information and draw appropriate diagrams.



Part AThe initial and final states of thetoolbox are illustrated in the figure. Identify the initial speed $v_i$ of the toolbox and thevertical distance through which the toolbox moves. Enter theinitial speed and theheight symbolically in terms of the variablesgiven in the problem introduction, separated by a comma.

$v_i$ , =

Answer 1

Well, first find the net accelerating force

Net accelerationforce= weight down the plane - friction
mgSinTheta - 22

Set that equal to mass*acceleration and solve for acceleration.

then:
Vfinal^2=Vinitial^2+2*a*d
(Vinitial is zero
solve for Vfinal