A little girl is riding a sled horizontally in the snow, the combined mass of the girl and sled is 33.4 kg. She is being pulled by her parents. Mom is pulling her with a force of 5.18 N, at an angle of 20.0 degree E of N. Dad is pulling her with a force of 11.15 N, at an angle of 33.7 degree W of N. There is a wind blowing with produces a force of 10.0 N to the east on the sled. (Use East as positive x and North as postive y)
a) What are the x and y components of the resultant force on the sled assuming the snow is frictionless?
b) What is the magnitude of the acceleration of the sled? [this one i can do if i can get a.]
c) What is the angle the acceleration of the sled makes with due North (using + for the east side and - for the west side)
(a) The x (East) component of the resultant force is:
Fx = 5.18 sin 20 - 11.15 sin 33.7 + 10.0
Add them up.
The y (North) component is:
Fy = 5.18 cos 20 + 11.15 cos 33.7
(There is no wind component)
Add them up.
(b) Use the Pythagorean theorem.
F = sqrt[(Fx)^2 + (Fy)^2]
a = F/m
(c) arctan Fx/Fy
To solve this problem, we can break down the forces acting on the sled into their x and y components. Once we have the components, we can use Newton's second law (F = ma) to calculate the acceleration of the sled. Let's go step by step:
a) To find the x and y components of the resultant force, we need to break down each force into its x and y components.
The force exerted by the mom can be broken down as follows:
Fx_mom = 5.18 N * sin(20.0°)
Fy_mom = 5.18 N * cos(20.0°)
The force exerted by the dad can be broken down as follows:
Fx_dad = 11.15 N * sin(33.7°)
Fy_dad = 11.15 N * cos(33.7°)
The force due to the wind blowing can be considered as acting only in the x direction since it's blowing horizontally:
Fx_wind = 10.0 N
Fy_wind = 0 N (there is no force in the y direction)
Now, to find the total x and y components:
F_total_x = Fx_mom + Fx_dad + Fx_wind
F_total_y = Fy_mom + Fy_dad + Fy_wind
b) To find the magnitude of acceleration (a), we can use Newton's second law (F = ma) along with the total resultant force obtained above.
F_total = sqrt(F_total_x^2 + F_total_y^2)
m = 33.4 kg
Using F_total = ma, we can solve for a:
a = F_total / m
c) To find the angle the acceleration of the sled makes with due North, we can use the arctan function:
angle = arctan(a_x / a_y)
In this case, a_x represents the x-component of the acceleration (which is the same as F_total_x), and a_y represents the y-component of the acceleration (which is the same as F_total_y).
Please note that the calculations for parts a), b), and c) may require a calculator or software to evaluate the trigonometric functions and perform the necessary arithmetic operations.