A baby carriage is moved horizontally to the beach area by applying a force = 8kg/F, making an angle of 30 degrees horizontally, knowing that the baby has a mass of 6kg. Calculate the magnitude of the effective component in which everyone knows less on the beach.
To solve this problem, we can break down the force into its horizontal and vertical components.
The given force is 8 kg/F, and it makes an angle of 30 degrees horizontally. The horizontal component of the force can be calculated using the cosine function:
Horizontal component = Force * cos(angle)
= 8 kg/F * cos(30 degrees)
= 8 * 0.866
= 6.928 kg/F
Since the baby carriage is moved horizontally, the vertical component of the force does not contribute to the movement of the baby carriage on the beach.
Therefore, the effective component in which everyone knows less on the beach is the horizontal component, which has a magnitude of 6.928 kg/F.
To calculate the magnitude of the effective component, we need to break down the applied force into its vertical and horizontal components.
Given:
Force applied, F = 8 kg/F
Angle, θ = 30 degrees
Mass of the baby, m = 6 kg
First, we need to find the horizontal component of the force (Fx) and the vertical component of the force (Fy).
The horizontal component (Fx) can be calculated using the formula:
Fx = F * cos(θ)
Substituting the given values:
Fx = 8 kg/F * cos(30 degrees)
= 8 kg/F * (√3/2)
≈ 6.928 kg/F
The vertical component (Fy) can be calculated using the formula:
Fy = F * sin(θ)
Substituting the given values:
Fy = 8 kg/F * sin(30 degrees)
= 8 kg/F * (1/2)
= 4 kg/F
Since we are interested in the effective component that everyone knows less on the beach, we can consider the vertical component of the force (Fy) as the effective component.
Therefore, the magnitude of the effective component is 4 kg/F.
To calculate the magnitude of the effective component of the force, we need to break down the given force into its horizontal and vertical components.
1. Start by finding the horizontal component of the force. This can be calculated using the formula: F_horizontal = F * cos(angle), where F is the given force and angle is the angle it makes with the horizontal.
In this case, the given force is 8 kg/F and the angle is 30 degrees.
F_horizontal = 8 kg/F * cos(30 degrees)
F_horizontal = 8 kg/F * (√3/2) (Note: cos 30 degrees = √3/2)
F_horizontal = 4√3 kg/F
2. Next, find the vertical component of the force. This can be calculated using the formula: F_vertical = F * sin(angle), where F is the given force and angle is the angle it makes with the horizontal.
Again, the given force is 8 kg/F and the angle is 30 degrees.
F_vertical = 8 kg/F * sin(30 degrees)
F_vertical = 8 kg/F * (1/2) (Note: sin 30 degrees = 1/2)
F_vertical = 4 kg/F
3. Now that we have the horizontal and vertical components of the force, we can calculate the effective component (F_effective) using the formula:
F_effective = √(F_horizontal^2 + F_vertical^2)
Substituting the values we calculated earlier:
F_effective = √((4√3 kg/F)^2 + (4 kg/F)^2)
F_effective = √(48 kg^2/F^2 + 16 kg^2/F^2)
F_effective = √64 kg^2/F^2
F_effective = 8 kg/F
Therefore, the magnitude of the effective component of the force is 8 kg/F.