dv, F dr nm ENAMPLE Comstant Net Force om a Fan Cart An easy way to apply a near
ID: 1884504 • Letter: D
Question
dv, F dr nm ENAMPLE Comstant Net Force om a Fan Cart An easy way to apply a nearly constant force is to mount a battery-powered fan on a cart (Figure 2.27). If the fan directs air backwards, the interaction with the air pushes the cart forward with a nearly constant force. (Airboats used in the very shallow Florida Everglades are built in a similar way, with large fans on top of the boats propelling them through the swamp.) Suppose that you have a fan cart whose mass is 0.5 kg. You turn on the fan, then give the cart a shove so that when it is at location (0.2,0,0) m it is traveling with velocity (0.3,0,0) m/s. At a time 0.9 seconds later, you observe that the cart is at location (0.146,0,0) m. What was the force exerted by the air on the Figure 2.27 A fan cart on a track. (Ruthfan cart? Chabay Bruce Sherwood) Solution Since both net force and motion are parallel to the track, we only need to consider the x components of position, velocity, and force. Using the equations derived above for the motion of a system that experiences a constant net force: s (m) 0.2 0.1 00146m-02m+(03msa9 s) 205 ke (09 s) A S DFGHUKExplanation / Answer
Solution:
Initial velocity = 0.3 m/s
use, S = So + ut + (1/2)at2
0.146 = 0.2 + 0.3(0.9) + (1/2)a(0.9)2
=> a = - 0.8 m/s2
now use F = ma
therefore, F = - 0.4 N
the negative sign indicates the direction of the force.
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