Astronauts in space move a toolbox from its initial position →=<15,14,−8>m to its final position →=<17,14,−1>m. The two astronauts each push on the box with a constant force. Astronaut 1 exerts a force 1→=<18,7,−12> and astronaut 2 exerts a force 2→=<16,−10,16>. Required:
What is the total work performed on the toolbox?

If both forces are measured in Newtons, then the net force is

F = (18, 7, -12) N + (16, -10, 16) N = (34, -3, 4) N

The toolbox undergoes a displacement (i.e. change in position) in the direction of the vector

d = (17, 14, -1) m - (15, 14, -8) m = (2, 0, -9) m

The total work done by the astronauts on the toolbox is then

F • d = (34, -3, 4) N • (2, 0, -9) m = (68 + 0 - 36) N•m = 32 J

grav force prop 1/r squared 2r all squared is 4rsquared 1/4rsquared quartered

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards