A block of mass m = 5.2 kg is pulled up a ? = 21 A block of mass m = 5.2 kg is p

Question

A block of mass m = 5.2 kg is pulled up a ? = 21

A block of mass m = 5.2 kg is pulled up a ? = 21A degree incline as in the figure with a force of magnitude F = 36 N. (a) Find the acceleration of the block if the incline is frictionless. Your response differs from the correct answer by more than 100%. m/s^2 (b) Find the acceleration of the block if the coefficient of kinetic friction between the block and incline is 0.12. Your response differs from the correct answer by more than 10%. Double check your calculations. m/s^2

Explanation / Answer

F(x)=ma
so you will get F-Wsin(21)=ma
substitute the values
i am taking gravity as 9.8 m/s2
36 - [5.2*(9.8)*(sin21)] = 5.2a

=> 36-18.26 = 5.2 a
=> a = 3.41 m/s2

for part B :

draw another free body diagram this time including the friction

N is the normal force perpendicular to the plane
F(y) = 0
N=Wcos(21)
f= friction
F= Force

and F(x)=ma
F- ( f + W sin21) =ma

now we dont have friction, but we know that f=uN, u = (coefficient of friction)

and we know that N = N=Wcos(21)
so that means, f= u(N) =uWcos(21)

substitute the values =>
f= 0.12(5.2*(9.8)cos21)
f= 5.71

Now to find the acceleration
as we know
F(x)=ma
F-( f + Wsin21) =ma

substitute the values =>
36 - ( 5.71 + 5.2*(9.8)sin21) = 5.2a

=> 36 - 23.97 = 5.2 a
=> a= 12.03/5.2
=> a= 2.31 m/s2

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