A luge and its rider, with a total mass of 90 kg, emerge from adownhill track on

Question

A luge and its rider, with a total mass of 90 kg, emerge from adownhill track onto a horizontal straight track with an initialspeed of 25 m/s. If a force slows them to a stop at a constant rateof 5.0 m/s2, (a) what magnitudeF is required for the force, (b) whatdistance d do they travel while slowing, and(c) what work W is done on them by theforce? What are (d)F,(e)d, and (f)Wif they, instead, slow at 10 m/s2?

(a)

Number

Units

(b)

Number

Units

(c)

Number

Units

(d)

Number

Units

(e)

Number

Units

(f)

Number

Units

(a)

Number

450

Units

N

Explanation / Answer

total mass m = 90 kg
Initial speed u = 25 m/s Accleration a = 5.0 m/s2 final speed v = 0 final speed v = 0 (a) magnitude F is requiredfor the force F = ma                                                                   = 90 * 5 = 450 N (b) distance d do theytravel while slowing from the relation v ^ 2- u ^ 2 = 2ad distance d= [ v ^ 2- u ^ 2 ] / 2a                 =62.5 m (c) work W is done on them by theforce = F d                                                               = 28125 J Accleration a ' = 10 m/s (d). force F ' = m a ' = 900 N (e). distance d do they travel while slowing from the relation v ^ 2- u ^ 2 = 2a 'd distance d ' = [ v ^ 2- u ^ 2 ] / 2a '                 = 31.25m (f). work W is done on them by the force = F 'd '                                                               = 14062.5 J from the relation v ^ 2- u ^ 2 = 2a 'd distance d ' = [ v ^ 2- u ^ 2 ] / 2a '                 = 31.25m (f). work W is done on them by the force = F 'd '                                                               = 14062.5 J                                                               = 14062.5 J

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