REFLECT Each of the three tensions is proportional tothe weight w if we double w
ID: 1552405 • Letter: R
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REFLECT Each of the three tensions is proportional tothe weight w if we double w, all three tensions double. Note that Ts is greater than the weight of the engine. If this seems strange, observe Tsmust be large enough for its vertical component to be equal in magnitude to w, so T sin 60 (-T) o w, we can rewrite the second equation as must have a magnitude larger than w. Because T Practice Problem: If we change the angle of the upper chain from 60 sin 60° 1.155 w. to 45 determine the new expressions for the three tensions. Answers w cos45°/sin 45 gKAMPLE 5.3 Car on a ramp ef176 x 104 N rests on the ramp of a trailer (Figure 5.3a). The car's brakes and transmission lock are re- AL Video Tutor Solution ased only the cable prevents the car from rolling backward off the trailer. The ramp makes an angle of 260 with the horizontal. Find the tension in the cable and the force with which the ramp pushes on the car's tires. We replace the weight by its components w sin (b) Free-body diagram for car (a) Car on ramp FIGURE 5.3 We orient our coordinate axes parallel and perpendicular to the ramp, SOLUTION and we replace the weight force by its find the components of UP Figure 5.3b shows our free-body diagram for the car. The car is in so we first Newton's first To three forces exerted on the car its weight the ten- soLVE e then apply between sion in the cable (magnitude T, and the normal force with magnitude n each force in our axis system and we note that the angle a by the ramp we the as we can find the components of the weight, lump the normal forces on the wheels together as a single force.)Explanation / Answer
here from the figure T = w sintheta
if T = w/2
w/2 = wsintheta
1/2 = sintheta
theta = sin^-1(1/2)
theta = sin^-1(sin30)
theta = 30 degrees
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