A 70.0-kg man stands on a pedestal of mass 27.0 kg, which rests on a level surface.
What is the normal force exerted by the ground on the pedestal?
A. 265 N
B. 368 N
C. 478 N
D. 624 N
E. 951 N
The Correct Answer and Explanation is:
To find the normal force exerted by the ground on the pedestal, we first need to understand the forces acting on the system, which consists of the man standing on the pedestal and the pedestal itself.
- Identifying the System: We have a man with a mass of ( m_1 = 70.0 \, \text{kg} ) standing on a pedestal with a mass of ( m_2 = 27.0 \, \text{kg} ).
- Calculating the Weight of Each Component: The weight of an object can be calculated using the formula: [
\text{Weight} = \text{mass} \times g
] where ( g ) (acceleration due to gravity) is approximately ( 9.81 \, \text{m/s}^2 ).
- For the man:
[
W_1 = m_1 \times g = 70.0 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 686.7 \, \text{N}
] - For the pedestal:
[
W_2 = m_2 \times g = 27.0 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 264.87 \, \text{N}
]
- Calculating the Total Weight: The total weight of the man and the pedestal combined is: [
W_{\text{total}} = W_1 + W_2 = 686.7 \, \text{N} + 264.87 \, \text{N} \approx 951.57 \, \text{N}
] - Understanding Normal Force: The normal force exerted by the ground on the pedestal (denoted as ( N )) must support the total weight of both the man and the pedestal. Since they are both resting on the ground, the normal force counteracts this combined weight.
- Final Calculation: Therefore, the normal force can be expressed as: [
N = W_{\text{total}} \approx 951.57 \, \text{N}
]
Thus, the normal force exerted by the ground on the pedestal is approximately 951 N. Therefore, the correct answer is E. 951 N. This calculation demonstrates how the weight of all objects in a system affects the normal force exerted by the surface they rest on, ensuring equilibrium within the system.