A toolbox is floating in an anti-gravity chamber. Two astronauts-in-training wor

Question

A toolbox is floating in an anti-gravity chamber. Two astronauts-in-training work together to maneuver the toolbox from its initial position r vector_1 = m to a more convenient position r vector_2 = m. The astronauts each pull on the box using a rope. Astronaut 1 exerts a force N. Astronaut 2 exerts a force N. (a) How much work is done by the two astronauts? (b) For each of the four scenarios sketched below, will the work done in the next instant be positive, negative or equal to zero? Place a check mark in the box or circle the correct answer below. (c) A charged particle of mass 2.2 times 10^-25 kg is accelerated by an external electric force to a speed of 2.1 times 10^6 m/s. What is its total energy? What is its kinetic energy? (d) Now a constant force is turned on that slows the charged particle from 2.1 times 10^6 m/s down to 1.8 times 10^6 m/s. During that time, the particle undergoes a displacement of 1000 m. Determine the component of the force that is parallel to the particle's displacement? Be sure to watch for sign errors.

Explanation / Answer

given initial location of toolbox, r1 = (20,14,5)
final position of toolbox, r2 = (20,10,-2)
displacement = r2 - r1 = (0,-4,-7)

a) Force by astronaut 1, F1 = (15,-3,-5) N
   force by astronaut 2, F2 = (7,14,-8) N
   now work done by a force for dislacementr s = F.s
   so, nwork done by astronaut 1, W1 = F1.(r2 - r1) = (15,-3,-5).(0,-4,-7) = 12 + 35 = 47 J
   similiarly, W2 = (7,14,-8).(0,-4,-7) = -56 + 56 = 0J
   so net work done by astronauts = 47 J
b) case 1: angle between P and F is acute, Work = F.p = Fpcos(theta)
     hence positive work
     case 2 : Angle is 90 deg, W = 0
     case 3 : angle is obtuse, Work is negative
     case 4: angle is obtuser, Worke is negative
c) m = 2.2*10^-25 kg
    v = 2.1*10^6 m/s
    total energy = mv^2 + 0.5mv^2 = 1445.3*10^-15 J
    KE = 0.5mv^2 = 485.1*10^-15 J

ionitial velocity, u = 2.1*10^6 m/s
final velocity, v = 1.810^6 m/s
displacememnt, s = 1000 m
so, 2as = v^2 - u^2
2*a*1000 = (1.810^2 - 2.1^2)*10^12
a = -566950000 m/s/s
Force = m*a = -12472.9*10^-20 N

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