A little girl is riding a sled horizontally in the snow, the combined mass of th

Question

A little girl is riding a sled horizontally in the snow, the combined mass of the girl and sled is 32.1kg . She is being pulled by her parents. Mom is pulling her with a force of 6.98N , at an angle of 18.6degree E of N. Dad is pulling her with a force of 11.79N , at an angle of 39.8degree W of N. There is a wind blowing with produces a force of 14.5N to the east on the sled. (Use East as positive x and North as postive y)

Part A:

What are the x and y components of Mom's force?

Part B:

What are the x and y components of the Dad's force?

Part C:

What are the x and y components of the resultant force on the sled assuming the snow is frictionless?

Part D:

What is the magnitude of the acceleration of the sled?

Part E:

What is the angle the acceleration of the sled makes with due North (using + for the east side and - for the west side)

Explanation / Answer

A)

F1x = 6.98*sin18 = 2.15 N

F1y = 6.98*cos18 = 6.63 N

B) F2x = -11.79*sin39.8 = -7.54 N

F2y = 11.79*cos39.8 = 9.05 N

C)

Fx = F1x + F2x + F3x = 2.15-7.54+14.5 = 9.11 N

Fy = F1y+F2y+F3y = 6.63 + 9.05 + 0 = 15.68 N

D) F net = sqrt(Fx^2 +Fy^2) =18.13 N

a = Fnet/m = 0.565 m/s^2 <-----answer

E) direction = tan^-1(Fx/Fy) = +30.16

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