Question

A stop block, s, prevents a crate from sliding down a 0 36.0° incline. (Figure 1) A tensile force F= (Fot) N acts on the crate parallel to the incline, where F 325 N/s If the coefficients of static and kinetic friction between the crate and the incline are 0.300 and 0.225 respectively, and the crate has a mass of 56.4 kg, how long will it take until the crate reaches a velocity of 2.07 m/s as it moves up the incline? = Express your answer numerically in seconds to three significant figures. View Available Hint(s) Πν ΑΣφ ? vec t= S Submit

Answer 1

Sole LT ngfing DIf VV mg mg oso F = mg sino +using coso) fot = mg Sine + us (mg caso) Hit=mg sjo+ us (mg caso) Fo = 56,4x9.81 Sch36' +0.3 X 56,4x4,81 COS 36 325 = 1.414 S When block is moving, ma = 325t - mg sino -uek (mg cose) du = 325t-mg Suhe -uk (mg cose) = 325t-56444.81 Su 36 -0,225 % 56,4*9.81 COS 36' 5614 = 325t – 425,926 5614 du = (5762€ -7.552) dt Integrate above,

sov = (5762t-7.552) dt V = $1762+2 -7,552t te At v=0&t=1,4145 0 = 5,762(1.414)-7552 (1,414) +C 2 c. C= 4.918 - V = 5.762+2 -7.552t +4,918 2.07 = 5.762 +2 -7.5525 +4.918 2 2 2,8812-7552+ + 2.848 = 0 By solving above quadratic eq? oe get t = 2.1655