a 75kg person is standing on a board inclined at 30 angle type the horizontal .what are the magnitudes of gravitational components normal to the board and parallel to the board
normal ... m g cos(30º)
parallel ... m g sin(30º)
To find the magnitudes of the gravitational components normal to the board and parallel to the board, we need to break down the weight of the person into its components.
The weight of the person can be calculated using the formula:
Weight = mass × acceleration due to gravity
Given that the person's mass is 75 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can find the weight:
Weight = 75 kg × 9.8 m/s^2
Weight = 735 N
Now, let's calculate the gravitational component parallel to the board. We can use trigonometry to determine this:
Gravitational component parallel to the board = Weight × sin(angle of inclination)
Gravitational component parallel to the board = 735 N × sin(30°)
Gravitational component parallel to the board ≈ 367.5 N
Finally, to find the gravitational component normal to the board, we use the equation:
Gravitational component normal to the board = Weight × cos(angle of inclination)
Gravitational component normal to the board = 735 N × cos(30°)
Gravitational component normal to the board ≈ 636.4 N
Therefore, the magnitudes of the gravitational components normal to the board and parallel to the board are approximately 636.4 N and 367.5 N, respectively.