Gravity and Vectors

3. An astronaut in his space suit has a total mass of 275 kg. His weight on the asteroid Erewhon is 0.3 N. What is the acceleration of gravity on Erewhon?
4. An electromagnetic mass driver subjects a 1 gm steel slug to an acceleration of 500 g. What force does the mass driver exert on the slug?
5. Four forces, represented by four vectors, are plotted in standard position on the Cartesian plane. The lengths of the vectors, in arbitrary units, represent the strength of the forces in N. The forces are being applied to an object with a mass of 10 kg, located at the origin. In what direction will the object accelerate, and how rapidly? The force vectors are A(10,5) B(3,-2) C(-1, 8) and D(-7,-3).

3. The weight G of an object is BY DEFINITION
$G = m*g$ where g is the acceleration of gravity
Hence $g = G/m = 0.3/275 =0.001091 m/s^2$

4. As the second law of physics states the Force is equal to the mass multiplied by the acceleration
$F = m*a = 10^{-3}*500*g=10^{-3}*500*9.81 = 4.905$ N

5. The x and y components of the forces adds algebraically. The forces are all located in origin (0,0) hence the x and y components of the forces are given in parenthesis.
$Fx =Ax+Bx+Cx+Dx = 10+3-1-7 =13-8 =5$
$Fy = Ay +By+Cy+Dy = 5-3+8-3 =13-6 = 7$
The total foces is $F =\sqrt{Fx^2+Fy^2} = \sqrt{25+49} =\sqrt{74} =8.60 N$
The direction (alpha is the angle made by the acceleration with the x axis) of the resulting acceleration is the direction of the force
$tan (\alpha) = Fy/Fx =7/5$
$\alpha = 54.46$ degree
The magnitude of the acceleration is
$a= F/m = 8.60/10 =0.86 m/s^2$