Question

Referring to the Interactive Figure below, suppose two astronauts are using jet packs to push a 940 kg satellite toward the space shuttle, as shown in the figure below. With the coordinate system indicated in the figure, astronaut #1 pushes in the positive x-direction and astronaut #2 pushes in a direction 52° above the x-axis. Astronaut #1 pushes with a force of magnitude F₁ = 26 N and astronaut #2 pushes with a force of magnitude F₂ = 45 N.

(a) Do you expect the direction of the satellite's acceleration to be greater than, less than, or equal to 32°?
(b) Find the direction of satellite's acceleration in this case.
___________ °
(c) Find the magnitude of the satellite's acceleration in this case.
___________ m/s²

Now, use what you have learned to answer the following. Suppose the satellite has a mass of 630, that astronaut #1 pushes with a force of magnitude F₁ = 55 N and that astronaut #2 pushes with a force of magnitude F₂ = 65 N in a direction 72° above the x-axis.

(d) Do you expect the direction of the satellite's acceleration to be greater than, less than, or equal to 41°?
(e) Find the direction of satellite's acceleration in this case.
___________ °
(f) Find the magnitude of the satellite's acceleration in this case.
___________ m/s²

Answer 1

Okay, let's find the components of F2

F2x = 45*cos 52

F2y = 45*sin 52

Similarly,

F1x = 26

F1y = 0

Now, add all the forces in x direction

Fx = 26 + 45*cos 52 = 53.7 N

Now, add all the forces in y direction

Fy = 0 + 45*sin 52

Fy = 35.46 N

Total net force

F = sqrt (53.7² + 35.46²)

F = 64.35 N

Therefore,

a = F/m

a = 64.35/940

a = 0.0685 m/s²

direction

theta = arctan (35.46 / 53.7)

theta = 33.44 degrees ( acceleration direction)

---------------------------------------------------------------------------------------------------------------

Solve in the same way,

Okay, let's find the components of F2

F2x = 65*cos 72

F2y = 65*sin 72

Similarly,

F1x = 55

F1y = 0

Now, add all the forces in x direction

Fx = 55 + 65*cos 72 = 75.1 N

Now, add all the forces in y direction

Fy = 0 + 65*sin 72

Fy = 61.8 N

net force = 97.27 N

acceleration = 0.154 m/s²

direction = 39.45 degree