The body

The body slides down an inclined plane forming an angle α = π / 4 = 45° under the action of a horizontal plane under the effect of friction forces with acceleration a = 2.4 m/s ^ 2. At what angle β must the plane be inclined so that the body slides on it after a small push at a constant speed?

Correct answer:

B =  33.1853 °

Step-by-step explanation:

α=π4=3.141640.7854 rad a=2.4 m/s2 g=9.81 m/s2  G=mg F1=ma=m g sinαm g k cosα ma=m g sinαm g k cosα a=g sinαg k cosα  k=(g sin(α)a)/(g cos(α))=(9.81 sin(0.7854)2.4)/(9.81 cos0.7854)0.654  a2=0 m/s2  g sinβg k cosβ=0 sinβk cosβ=0 sinβ/cosβk=0 tanβk=0  β=arctan(k)=arctan(0.654)0.5792 rad  B=β=β 180π=0.5792 180π=33.185=33.1853=33117"

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