Question

1a.Diane (weight 255 N)is practicing on a tightrope that is 6.00 meters long and sags by 0.120 meters. When she is in the middle of the rope, what is the force on eacheyebolt holding the tightrope?

1b. Vector A has a magnitude of 3.0 units and makes an angle of -90.0 degrees with the positive x-axis. Vector B has a magnitude of 4.0 units and makes and angle of-120 degrees with the positive x-axis. What is the direction of the vector sum A+B referenced to the positive x-axis?

1c.The moon with a mass of 7.35 *10^22kg is orbiting about the earth with a mass of 5.98*10^24kg at a radius of 3.85*10^8 meters.The earth is orbiting about the sunwith a mass of 1.99*10^30kg at a radius of 1.50*10^11 meters.The gravitational field on the moon due to the earth and the sun when it is between them is (G=6.67*10^-11 N m^2/kg^2)

Answer 1

T*sin (theta)+T*sin(theta)-255=0

so 255/2*sin(theta)= T

T= 3.19 x 103 N

Answer 2

Vector A has a magnitude of 3.0 units and makes an angle of -90.0 with the positive x-axis
this means it is along negative y -axis
A = -3 j

B makes -120 means it is in 3rd quadrant ,60 degrees below neagtive x-axis

B = -(4cos(60)+4sin(60)) = - 2 i - 2√3 j

A + B = -2 i -(3+2√3) j

both i ,j componets are negative

so vector is in 3rd quadrant

it is below x axis by an angle θ

tan(θ)=|-(3+2√3)|/|-2| = 72.8

ans shoud be -(180-72.8) = -107.2

Answer 3

Gravitational force F_G = G Mm/ r² Newton , and is acting along the line connecting the masses M and m.

G= 6.67*10^-11 N m²/kg²

mass of moon m_m= 7.35*10²² kg

mass of earth, m_e = 5.98*10²⁴ kg

radius of orbit of moon around earth r_me = 3.85*10⁸ meters

mass of sun M_s = 1.99*10³⁰ kg

radius of orbit of earth around sun r_es = 1.50*10¹¹ meters.

So the distance between moon and sun when moon is in between sun and earth r_ms = r_es - r_me

r_ms = 1.50*10¹¹ - 3.85*10⁸ = 1.496*10 ¹¹ m

When moon is in between earth and sun, both will attract moon, So the total force

Ftotal =F_{sun- moon} - F_{earth- moon}

= (G M_sm_m/ r_ms² ) - (G m_em_m/ r_me² ) = 2.38* 10²⁰ N towards sun