14. Two forces act on a 55kg object. One force has magnitude of 65N directed 59

Question

14. Two forces act on a 55kg object. One force has magnitude of 65N directed 59 degrees clockwise from the positive x axis and the other has a magnitude of 35N at 32 degrees clockwise from the positive y axis. what is the magnitude of the objects acceleration and in what direction? if the object started at rest, what is its velocity after 10seconds?

15. The international space station has a mass of 1.8 X 10^5kg. a 70.0kg astronaut outside the station pushes off one wall of the station so she can accelerate at 1.50m/s2. what is the magnitude of the acceleration of the space station as the astronaut is pushing off the wall. Give your answers relative to an observer who is space walking and therefore does not accelerate with the space station due to push.

Explanation / Answer

(a)

force 1: x component = 65cos59 = 33.5N
y component = -65sin59=-55.7N (if the angle is clockwise from the +x axis, the y component is negative:

force 2: x component = 35sin 32=18.5N
y component = 35 cos32=29.7N

total x component=52N
total y component-26N

total magnitude of force =sqrt[52^2 +(-26)^2]
total mag of force = 58.1N

therefore, the total acceleration is a= F/m=58.1/55=1.06m/s^2

from vf = vi + at

vf= 1.06*10 = 10.6 m/s

(b)

to accelerate to 1.5m/s^2 the astronaut had to push with a force of

F=MA
=70kg (1.5m/s^2)
= 105 N

the same force was applied to the spacestation.
F=MA
105 = 1.8x 10^5 A

A= 5.8 x 10^-4 m/s^2

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