131_PartUniversity Physics Solution

131_PartUniversity Physics Solution - Applying Newtons Laws...

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Applying Newton&s Laws 5-3 5.6. IDENTIFY: Apply Newton&s 1st law to the car. The forces are the same as in Example 5.5. SET UP: The free-body diagram is sketched in Figure 5.6. EXECUTE: x x Fm a = cos sin 0 Tn α = cos sin = y y a = cos sin 0 nTw + −= cos sin + = Figure 5.6 The first equation gives cos . sin nT ⎛⎞ = ⎜⎟ ⎝⎠ Use this in the second equation to eliminate n : cos cos sin sin TT w αα + = Multiply this equation by sin : 22 (cos sin ) sin Tw += sin = (since cos sin 1 ). Then cos cos sin cos . sin sin w w == = EVALUATE: These results are the same as obtained in Example 5.5. The choice of coordinate axes is up to us. Some choices may make the calculation easier, but the results are the same for any choice of axes. 5.7. IDENTIFY: Apply m = F a ! ! to the car. SET UP: Use coordinates with x + parallel to the surface of the street. EXECUTE: 0 x F = gives sin = . 23 sin (1390 kg)(9.80 m/s )sin17.5 4.10 10 N g θ ° = × . EVALUATE: The force required is less than the weight of the car by the factor sin . 5.8. IDENTIFY: Apply Newton&s 1st law to the wrecking ball. Each cable exerts a force on the ball, directed along the cable. SET UP: The force diagram for the wrecking ball is sketched in Figure 5.8. Figure 5.8 EXECUTE: (a) y y a = cos40 0 B Tm g °− = 2 4 (4090 kg)(9.80 m/s ) 5.23 10 N cos40 cos40 B mg T = × °° (b) x x a = sin40 0 BA = 4 sin 40 3.36 10 N AB = × EVALUATE: If the angle 40 ° is replaces by 0 ° (cable B is vertical), then B g = and 0. A T =
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5-4 Chapter 5 5.9. IDENTIFY: Apply m = F a ! ! to the object and to the knot where the cords are joined. SET UP: Let y + be upward and x + be to the right. EXECUTE: (a) , sin30 sin45 , and cos30 cos45 0. CA B C A B T w TTT w TT + ° = = ° ° = Since sin45 cos45 , °= ° adding the last two equations gives (cos30 sin30 ) , A Tw °+ ° = and so 0.732 . 1.366 A w == Then, cos30 0.897 .
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This note was uploaded on 07/16/2011 for the course PHY 2053 taught by Professor Buchler during the Spring '06 term at University of Florida.

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131_PartUniversity Physics Solution - Applying Newtons Laws...

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