HW4_solution

# HW4_solution - t-tw~4 PROBLEM 13.144;6 An estimate of the...

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Unformatted text preview: t-tw~4 PROBLEM 13.144 ;6 An estimate of the expected load on over-the-shoulder seat belts is made before designing prototype belts that will be evaluated in automobile crash tests. Assuming that an automobile traveling at 72 km/h is brought to a stop in 110 ms, determine (a) the average impulsive force exerted by a 100-kg man on the belt, (b) the maximum forceFm exerted on the belt if the force-time diagram has the shape shown. SOLUTION (a) Force on the belt is opposite to the direction shown. VI = 72 km/h = 20 mis, m = 100kg ( 100 kg) (20 mls)- Fave (0.11 0 s) = 0 /).t = 0.11 0 s ( 100 )( 20 ) F = = 18182 N aye ( 0.110 ) Fave = 18.18 kN ~ (b) Impulse = area under F- t diagram 1 = -Fm(0.110s) 2 F (N) Fill 110 f (ms) From (a) = (18182 N) (0.110 s) !Fm(0.110) = 18182(0.110) 2-- PROBLEM 13.152 t 2m 1___ In order to test the resistance of a chain to impact, the chain is suspended from a 120-kg rigid beam supported by two columns. A rod attached to the last link is then hit by a 30-kg block dropped from a 2-m height. Determine the initial impulse exerted on the chain and the energy absorbed by the chain, assuming that the block does not rebound from the rod and that the columns supporting the beam are (a) perfectly rigid, (b) equivalent to two perfectly elastic springs. SOLUTION Before impact 1] = 0, VI = mgh = (30 kg)(9.81 m/s2)(2 m) = 588.6 N 1 2 T2 = "2 mv , V2 = 0 1] + VI = T2 + V2: 588.6 = ~(30 )v2. ~ v = 6.2642 m/s 2 (a) Rigid columns ~ + + t-mv + FI1t = 30(6.2642) = F /).t Fl1t = 187.93N.s t on the block F I1t...
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HW4_solution - t-tw~4 PROBLEM 13.144;6 An estimate of the...

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