To find the direction of acceleration in degrees, we first need to break down the given forces into their horizontal (x-axis) and vertical (y-axis) components.
Given forces:
- Force 1: 11.1N north
- Force 2: 19.9N east
- Force 3: 14.0N south
To find the horizontal and vertical components of each force, we need to use trigonometry. Since north is opposite to the y-axis and east is opposite to the x-axis, we can use the following trigonometric functions:
- Horizontal (x-axis) component: cos(angle) = adjacent/hypotenuse
- Vertical (y-axis) component: sin(angle) = opposite/hypotenuse
Here's how we can calculate the horizontal and vertical components for each force:
Force 1:
- Horizontal component: 0N since it is purely in the vertical direction (north)
- Vertical component: 11.1N (opposite/hypotenuse)
Force 2:
- Horizontal component: 19.9N (adjacent/hypotenuse)
- Vertical component: 0N since it is purely in the horizontal direction (east)
Force 3:
- Horizontal component: 0N since it is purely in the vertical direction (south)
- Vertical component: -14.0N (opposite/hypotenuse) Note: Negative sign indicates the direction is opposite to the positive y-axis.
Now, let's calculate the total horizontal and vertical components:
Total horizontal component = Sum of all the horizontal components
= 0N + 19.9N + 0N
= 19.9N
Total vertical component = Sum of all the vertical components
= 11.1N + 0N + (-14.0N)
= -2.9N
Next, we can use the components to find the magnitude and angle of the acceleration.
Magnitude of acceleration:
The magnitude of acceleration can be obtained using the equation:
acceleration = net force / mass
Given that the net force is the vector sum of all forces, we can calculate it using the Pythagorean theorem:
net force = √((total horizontal component)^2 + (total vertical component)^2)
net force = √((19.9N)^2 + (-2.9N)^2)
net force = √(396.01N^2 + 8.41N^2)
net force = √(404.42N^2)
net force = 20.11N
Acceleration = net force / mass
Acceleration = 20.11N / 3.62kg
Acceleration ≈ 5.55 m/s^2 (rounded to two decimal places)
Now, to find the direction of acceleration in degrees, we can use the inverse tangent function with the total horizontal and vertical components:
Angle of acceleration (θ) = tan^(-1)(total vertical component / total horizontal component)
Angle of acceleration (θ) = tan^(-1)(-2.9N / 19.9N)
θ ≈ -8.7 degrees (rounded to one decimal place)
Therefore, the direction of the acceleration is approximately -8.7 degrees.