Figure 1: A cost-free body diagram for package of books. We have the right to imagine act the complying with experimentsand noting the outcomes:1. A 1 kg mass is increased at 1 m/s ~ above the waiting track and also theforce forced is found to it is in 1 N (in the direction that the acceleration).Since the air track pushes increase on the mass come balance the force of gravity andthere is no friction, the net, unbalanced force on the mass is 1 N.2. The 1 kg fixed is accelerated at 2 m/s on the wait track and the forceis discovered to be 2 N. In ~ 5 m/s, the force is found to be 5 N.3. The 1 kg fixed is hung indigenous the feather scale and remains stationary.The force is 9.8 N. In this case, there is no acceleration so the netforce is zero, i.e. The force of heaviness is well balanced by the upwardpull the the scale. The force exerted by the spring scale should thereforebe same in magnitude, despite opposite in direction come the pressure exerted bygravity. (In truth the fixed is being weighed, and the load is 9.8 N.)If the mass to be pulled follow me the airtrack through this force, what wouldits acceleration be?4. The ahead experiment is perform in one elevator. If the elevator isaccelerating upward at 2 m/s, the pressure is 11.8 N. If the elevator isaccelerating downward at 3 m/s, the force is 6.8 N.5. Every of the preceeding experiments is performed through a mass of 2 kg and5 kg and also the force is found to it is in respectively2 times and 5 times that for the 1 kg mass.In the previous experiments, the 1 kg mass increased only if a net, unbalancedforce to be exerted. If there existed together a network force, the acceleration, the massand the pressure are related as follows:.Let"s make certain this is the case for every experiment. In 1.), the unit offorce 1 Newton is characterized as the net pressure exerted ~ above 1 kg accelerating at1 m/s. Native 2.) we view that this pressure is proportional to the acceleration and also from5.) that it is proportional come the mass.Experiment 3.) is different. In this case, we room measuring the force neededto balance the pressure of gravity and also so the net force is the vectorsum of gravity and also that that the scale: . Because gravitypulls down and also the range pulls up, we deserve to express this in terms of the contents in the vertical direction as and also note the .Finally, together expected, we have actually . The forceof heaviness is because of this 9.8 N, 19.6 N and 49 N respectively for the 1 kg, 2 kg and also 5 kg masses, that is 9.8 m/s time the mass. = mg (g = 9.8 m/s 10 m/s).From the connection of force, massive andacceleration, what would be the accelerations that these 3 masses if thespring scale were removed?The experiment 4.), performed in the elevator relates to her experience.When the elevator beginning upward, you feel a bit "heavier" as itaccelerates and as the starts downward, you feel a little bit "lighter."We can now consider this quantitatively: wherein is either 2 m/s increase or 3 m/s downward.Let"s fix for . Because that the 1 kg massaccelerating upward at 2 m/s, = 9.8 N and also = 2 N + 9.8 N = 11.8 N.
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For the mass increasing downwardat 3 m/s (a = -3 m/s), = -3 N + 9.8 N = 6.8 N. Go back to Physics 125