Please show all work. A student, crazed by the combined stress of work, classes

Question

Please show all work.

A student, crazed by the combined stress of work, classes and an upcoming Thanksgiving where she will have to talk politics with her family, finally cracks and starts pushing a block across the ceiling yelling "I've got your normal force right here!" The block has a mss of 5.0 kg, and the force of the stu dent's push is P, directed as shown. The coefficients of static and kinetic friction between the block and the ceiling are 0.35 and .-0.65, respectively. 70° a) What is the smallest magnitude the force P could have which would cause the block to start moving? b) If the student pushes with her maximum force (130 N), what will the acceleration of the block be imme diately after it begins moving? a) b)

Explanation / Answer

(1)

Apply Newton second law

p- fs = ma

before starting a= 0

p = fs

= us N

here N+ p sin theta = mg

N = mg - p sin theta

p = us ( mg- p sin theta)

= us mg - us p sin theta

p+ us p sin theta= us mg

p(1+ us sin theta)= us mg

p = us mg/ 1+ us sin theta)

=0.65(5)(9.8)/ ( 1+ 0.65 sin 70)

=19.77 N

(b)

p- fk = ma

p - uk N = ma

p- uk ( mg- p sin theta) = ma

p- uk mg - uk p sin theta = ma

a= p- uk mg - uk p sin theta/m

=130-0.35( 5) (9.8) - 0.35 ( 130) sin 70/5

=14 m/s^2

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