Fred the otter climbed to the top of an inclined plane. His friend, Giselle the giraffe, suggested that he was so small that gravity would ignore him and he would be unable to slide down. "On the contrary", said Fred, "Since this slope makes an angle of 48.4 degrees with the horizontal and I have a mass of 3.8 kilograms, the magnitude of the component of my weight that acts parallel to the slope is equal to..." Fred knew how to calculate this, can you? Please enter the magnitude of the component of Fred's weight that is parallel to the incline in Newtons. DO NOT ROUND
To find the magnitude of the component of Fred's weight that acts parallel to the slope, we need to use the concept of trigonometry and resolve the weight vector into its components.
The weight of an object can be calculated using the equation W = m * g, where W is the weight, m is the mass, and g is the acceleration due to gravity.
In this case, Fred's mass is given as 3.8 kilograms. We can assume the acceleration due to gravity is approximately 9.8 m/s².
So, the weight of Fred can be calculated as:
W = 3.8 kg * 9.8 m/s²
W ≈ 37.24 N
Now, to find the component of the weight that acts parallel to the inclined plane, we use the equation:
F_parallel = W * cos(theta)
Here, theta is the angle of the inclined plane, given as 48.4 degrees.
First, we need to convert the angle to radians since the trigonometric functions in most programming languages expect the angle in radians.
To convert degrees to radians, we use the formula:
radians = degrees * pi / 180
So, converting the angle:
theta_radians = 48.4 degrees * pi / 180
theta_radians ≈ 0.845 radians
Now, we can calculate the component of Fred's weight that acts parallel to the slope:
F_parallel = 37.24 N * cos(0.845 radians)
F_parallel ≈ 37.24 N * 0.664
F_parallel ≈ 24.70696 N
Therefore, the magnitude of the component of Fred's weight that acts parallel to the slope is approximately 24.70696 Newtons.