Review. Two identical hard spheres, each of mass m and radius r , are released from rest in otherwise empty space with their centers separated by the distance R . They are allowed to collide under the influence of their gravitational attraction. (a) Show that the magnitude of the impulse received by each sphere before they make contact is given by [ Gm 3 (1/2 r − 1/ R ) 1/2 . (b) What If? Find the magnitude of the impulse each receives during their contact if they collide elastically.
Review. Two identical hard spheres, each of mass m and radius r , are released from rest in otherwise empty space with their centers separated by the distance R . They are allowed to collide under the influence of their gravitational attraction. (a) Show that the magnitude of the impulse received by each sphere before they make contact is given by [ Gm 3 (1/2 r − 1/ R ) 1/2 . (b) What If? Find the magnitude of the impulse each receives during their contact if they collide elastically.
Solution Summary: The author explains how two identical hard spheres are released from rest in otherwise empty space with their centers separated by the distance R.
Review. Two identical hard spheres, each of mass m and radius r, are released from rest in otherwise empty space with their centers separated by the distance R. They are allowed to collide under the influence of their gravitational attraction. (a) Show that the magnitude of the impulse received by each sphere before they make contact is given by [Gm3(1/2r − 1/R)1/2. (b) What If? Find the magnitude of the impulse each receives during their contact if they collide elastically.
Two identical hard spheres, each of mass m and radius r, are released from rest in otherwise empty space with their centers separated by the distance R. They are allowed to collide under the influence of their gravitational attraction. (a) Show that the magnitude of the impulse received by each sphere before they make contact is given by [Gm3(1/2r - 1/R)]1/2. (b) What If? Find the magnitude of the impulse each receives during their contact if they collide elastically.
A spaceship has length 120 m, diameter 25 m, and mass 4.0 x 103 kg as measured by its crew. As the spaceship moves parallel to its cylindrical axis and passes us, we measure its length to be 90 m. (a) What do we measure its diameter to be? (b) What do we measure the magnitude of its momentum to be?
Bryce, a mouse lover, keeps his four pet mice in a roomy cage, where they spend much of their spare time joyfully scampering
about on the cage's floor. Bryce tracks his mice's health diligently and just now recorded their masses as m₁ = 0.0145 kg,
m2 = 0.0141 kg, m3 = 0.0245 kg, and m4 = 0.0105 kg.
At this very instant, the x and y components (Ux, U,) of the mice's velocities are, respectively,
(U₁x, U₁₁y) = (0.591 m/s, -0.425 m/s,) (v2.x, U2,y) = (-0.605 m/s, -0.933 m/s,) (v3,x, U3,y) = (0.259 m/s, 0.305 m/s), and
(V4x, V4,y) = (-0.211 m/s, 0.569 m/s).
Calculate the x and y components px and py of Bryce's mice's total momentum.
Px =
kg.m/s
Py =
kg.m/s
Chapter 13 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
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