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 calculate the magnitude of the component of Fred's weight that acts parallel to the slope, you can use the following formula:
Component of weight parallel to slope = weight * sin(angle)
First, we need to determine the weight of Fred, which is equal to his mass multiplied by the acceleration due to gravity. The acceleration due to gravity is approximately 9.8 m/s².
Weight = mass * acceleration due to gravity
Weight = 3.8 kg * 9.8 m/s²
Now, we can calculate the magnitude of the component of Fred's weight that acts parallel to the slope using the formula mentioned earlier.
Component of weight parallel to slope = 3.8 kg * 9.8 m/s² * sin(48.4°)
Using a scientific calculator, the value of sin(48.4°) is approximately 0.746.
Component of weight parallel to slope = 3.8 kg * 9.8 m/s² * 0.746
Simplifying this calculation gives us:
Component of weight parallel to slope ≈ 27.3624 N
Therefore, the magnitude of the component of Fred's weight that acts parallel to the incline is approximately 27.3624 Newtons.