Item 6 Part A The two trees in the figure are 70 m apart A b

Item 6 Part A The two trees in the figure are 7.0 m apart. A back-packer is trying to litt his pack out of the reach of bears. (Fioure 1) Calculate the magnitude or the force F that he must exert downward to hold a 20-kg backpack so that the rope sags at its midpoint by 1.7 m. Ignore the friction between the rope and the branch on the left. Express your answer using two significant figures. Submit My Answers Give Up Part B Calculate the magnitude of the force F that he must exert downward to hold a 20-kg backpack so that the rope sags at its midpoint by 0.15 m Expres Figure 1 01 1 s your answer using two significant figures. Submit My Answers GMe Up Continue

Solution

Applying Newton’s 2^nd law vertically,

Fnety=ma

T1y+T2y - mg = ma = 0

From (1),

Tsin + Tsin = mg

2Tsin=mg

T= mg/(2sin) -------------(2)

Applying Newton’s 2^nd law to the hand of back-packer

F – T = ma = 0

F = T ----------(3)

From (2),

F = mg/(2sin) -----------(4)

A)

Let us find

We have

D=7.0/2=3.5m, d=1.7m, m=20kg

tan=d/D

=tan^-1(d/D)

=tan^-1(1.7/3.5)=25.91 deg

Plugging these values in eqn (4),

F = (20.0*9.8)/(2*sin25.91)

F = 220 N

B)

Let us find

We have

D=7.0/2=3.5m, d= 0.15m, m=20kg

tan=d/D

=tan^-1(d/D)

=tan^-1(0.15/3.5)=2.454 deg

Plugging these values in eqn (4),

F = (20.0*9.8)/(2*sin2.454)

F = 2300 N