If the speed of the cart at x1 were not zero but 65 cm/s, what would the speed b

Question

If the speed of the cart at x1 were not zero but 65 cm/s, what would the speed be at x2? Revised speed v(x2) = What is the speed v of the cart at x2? Speed v(x2) = If the force F(x) is linear, as shown in the graph, what is the work W done by the spring between x1 and x2? W = A cart of mass m = 0.7 kg is that includes a force sensor is attached to a spring connected to a backstop. The cart is pulled toward a motion sensor, held for a moment, and released. The force sensor records the force from the spring while the cart is moving, and the computer plots this force F(x) as a function of of position x from the motion sensor, as shown in the figure. At x1 = 28 cm, F1 = 3.8 N, and at x2 = 60 cm, F2 = 1.3 N. (Watch sigfigs

Explanation / Answer

1) Work = Force * displacement
Basically, since the graph you have here is a F-x graph, the shaded area is the work done by spring.

(Area in F-x graph is Area = F*x = W)

So Work = (F1+F2)*(x2-x1)/2 = (3.8+1.3)*(0.60 - 0.28 )/2 = 0.816 J

2) W = change in kinetic energy

W = 0.5*m*v2 - 0 = 0.5*(0.7)* v2 = 0.816

Thus, v = [0.816/(0.5*0.7)] = 1.527 m/s

3) 65 cm/s = 0.65 m/s

(Since I use SI unit throughout, it's better to convert to SI unit to avoid possible mistakes)

W = 0.5*0.7*v2 - 0.5*0.7*0.652 = 0.816

v =[ (0.816 + 0.5*0.7*0.652)/(0.5*0.7) ] = 1.66 m/s

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