Chapter 05, Problem 005 Three astronauts, propelled by jet backpacks, push and g

Question

Chapter 05, Problem 005 Three astronauts, propelled by jet backpacks, push and guide a 112 kg asteroid toward a processing dock, exerting the forces shown in the figure, with F1 30 N, F2-55 N, F3 41 N, 1-30°, and 63 60o. What is the (a) magnitude and (b) angle (measured relative to the positive direction of the x axis in the range of (-180°, 180°]) of the asteroid's acceleration? Chapter 05, Problem 009 A 0.27 kg particle moves in an xy plane according to x(t)13 2 t- 6 t3 and y(t) 245t- 8 t2, with x and y in meters and t in seconds. Att 1.0 s, what are (a) the magnitude and (b) the angle (within (-180°, 180°] interval relative to the positive direction of the x axis) of the net force on the particle, and (c) what is the angle of the particle's direction of travel? (a) Number Units (b) Number Units (e) Number Units

Explanation / Answer

a)

Fnetx = F1x+F2x+F3x = 30cos30 + 55cos0 + 41cos60 = 101.48 N

anetx = Fnetx/m = 101.48/112 = 0.906 m/s2

Fnety = F1y+F2y+F3 = 30sin30 + 55sin0 – 41sin60 = -20.51 N

anetx = Fnetx/m = -20.51/112 = 0.18 m/s2

anet = anetx i^+ anetyj^ = (0.906i^-0.18j^)

b)

|Fnet|= sqrt(Fnet2 + Fnety2) = sqrt(0.906^2+0.18^2) = 0.92 N

c)

=tan^-1(Fnety/Fnetx) = tan^-1(-0.18/0.906) = -11.24o ….clockwise from +X axis

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.