5. Which of the following forces is not conservative? (A)F=3+4)(B)F=3xi+4y(C)F=3y+4x(D)F=3x2+4y2 Solutio The work done by the force in(C)is Fdi=3ydr+]4xdy, the result of this integration depends on the rout of the path I. filling the blanks 1. A chain is held on a frictionless table with one-fourth FEEEEEEEEEEEERE of its length hanging over the edge, as shown in Fig. 1. If the chain has a length L and a mass m, the work required to pull the hanging part back on the table is mgL/32 Solution Since Conserv =-APE, if we choose the zero potential energy on the table the work required to pull the hanging part back on the table is W gh L L a forc system has only -component Fr; a graph of this compone FN 30 Irc function of position gure 2. The work done by this force if the 20 system moves along the x-axis from x=0 m to x= 10.0 m is 235.5 J x(m) 100 The work done by this force is the Fig 2 curve between x=0 m and 丌(30N)(5m)=75=235.5→W=235.5J 3. A 2. 14kg block is dropped from a height of 43 6cm onto a spring of force constant k=186N/cm, as shown in Fig 3. The maximum 43.6cm ill be Solution Using conversation of energy, assume the gravitational potential Fig 35. Which of the following forces is not conservative? （ C ） (A) F i j = 3ˆ + 4 ˆ r (B) F xi yj = 3 ˆ + 4 ˆ r (C) F yi xj = 3 ˆ + 4 ˆ r (D) F x i y j 3 ˆ 4 ˆ 2 2 = + r Solution The work done by the force in (C) is ∫ ∫ ∫ ⋅ = + f i f i x x y y F dr 3ydx 4xdy v v , the result of this integration depends on the rout of the path. II. Filling the Blanks 1. A chain is held on a frictionless table with one-fourth of its length hanging over the edge, as shown in Fig.1. If the chain has a length L and a mass m, the work required to pull the hanging part back on the table is mgL/32 . Solution: Since Wconserv = −∆PE , if we choose the zero potential energy on the table the work required to pull the hanging part back on the table is W mgh mg L mgL 32 1 8 1 4 1 conserv = = ⋅ = 2 A force on a system has only an x-component Fx; a graph of this component as a function of position x is shown in Figure 2. The work done by this force if the system moves along the x-axis from x = 0 m to x = 10.0 m is 235.5 J . Solution: The work done by this force is the area under the curve between xi = 0 m and x f =10 m (30N)(5m) 75 235.5 235.5 J 2 1 area = π = π = ⇒ W = 3. A 2.14kg block is dropped from a height of 43.6cm onto a spring of force constant k=18.6N/cm, as shown in Fig.3. The maximum distance the spring will be compressed is 11.1cm . Solution: Using conversation of energy, assume the gravitational potential x(m) Fx(N) Fig.2 5.0 10.0 10 20 30 Circle Fig.1 k 43.6cm Fig.3