The figure gives the acceleration of a 4.0 kg particle as an applied force moves
ID: 2034710 • Letter: T
Question
The figure gives the acceleration of a 4.0 kg particle as an applied force moves it from rest along an x axis from x = 0 to x = 9.0 m. The scale of the figure's vertical axis is set by as = 8.0 m/s2. How much work has the force done on the particle when the particle reaches (a) x = 4.0 m, (b) x = 7.0 m, and (c) x = 9.0 m? What is the particle's speed and direction (give positive answer if the particle moves along x axis in positive direction and negative otherwise) of travel when it reaches (d) x = 4.0 m, (e) x = 7.0 m, and (f) x = 9.0 m?
Explanation / Answer
a)
A = area at x = 4 , = (0.5) (8) (1) + (4 - 1) (8) = 28
Work done = m x area under acceleration-displacement graph = 4 x 28 = 112 J
b)
x = 7 m
A = area at x = 7 , = (0.5) (8) (1) + (4 - 1) (8) + (0.5) (8) (1) - (0.5) (8) (1) = 28
Work done = m x area under acceleration-displacement graph = 4 x 28 = 112 J
c)
x = 9 m
A = area at x = 9 , = (0.5) (8) (1) + (4 - 1) (8) + (0.5) (8) (1) - (0.5) (8) (1) + (2) (- 8) - (0.5) (8) (1) = 8
Work done = m x area under acceleration-displacement graph = 4 x 8 = 32 J