Question

You've just put a new wood floor in your house. An object will dent the flooring if the stress--the force divided by the area--exerted by the object is great enough. What stress is caused by a 5000 kg african elephant (40- cm -diameter foot pads) standing on all four legs?

Answer 1

To find the stress caused by a 5,000 kg African elephant with 40 cm diameter foot pads, we calculate the elephant's weight and divide it by the area of the foot pads. The stress is approximately 98,100 N/m2 or Pascals (Pa).

Step-by-step explanation:

To calculate the stress exerted by a 5,000 kg African elephant with 40 cm diameter foot pads standing on all four legs on a wood floor, we can use the formula: stress = force / area. The force is due to the elephant's weight, which is the product of its mass and the acceleration due to gravity (g = 9.81 m/s2). Four foot pads support this weight.

First, calculate the weight (force) of the elephant:

• Weight = Mass × g
• Weight = 5,000 kg × 9.81 m/s2
• Weight = 49,050 N (rounded to three significant digits).

Next, convert the diameter of the foot pad to radius and find the area:

• Radius = Diameter / 2 = 40 cm / 2 = 20 cm = 0.2 m
• Area = π × radius2 = 3.14159 × (0.2 m)2 = 0.1256 m2 (per foot)

Divide the weight by the area of one foot pad to find the stress per foot:

• Stress = Weight / (Area × 4) since the weight is supported by four feet
• Stress = 49,050 N / (0.1256 m2 × 4)
• Stress ≈ 98,100 N/m2 or Pascals

This is the stress that each foot pad would exert on the wood floor.