A diver of mass 68.9 kg stands at the end of a diving board of mass 24.5 kg and length L = 3.29 m. The diving board is supported at two locations, labeled A and B on the diagram. A and B are separated by a distance d = 0.74 m. Observe normal sign conventions for vertical forces.
What is the support force at A?
96
To determine the support force at point A, we need to consider the equilibrium of forces acting on the diving board.
1. Start by considering the forces acting vertically:
- The weight of the diver acts downward with a magnitude of m₁ * g, where m₁ is the mass of the diver and g is the acceleration due to gravity.
- The weight of the diving board acts downward with a magnitude of m₂ * g, where m₂ is the mass of the diving board.
- The support force at point A acts upward.
2. Since the diving board is in equilibrium (not accelerating vertically), the sum of the vertical forces must be zero:
ΣFy = 0
3. Apply Newton's second law for vertical equilibrium:
ΣFy = N - m₁ * g - m₂ * g = 0
4. Rearrange the equation to solve for the support force at point A (N):
N = m₁ * g + m₂ * g
5. Substitute the given values into the equation:
N = (68.9 kg) * (9.8 m/s²) + (24.5 kg) * (9.8 m/s²)
6. Calculate the support force at point A:
N = 674.62 N + 240.1 N
N ≈ 914.72 N
Therefore, the support force at point A is approximately 914.72 newtons.