Steel is very stiff, and the Young's modulus for steel is unusually large, 2.0×1011 N/m2. A cube of steel 25 cm on a side supports a load of 85 kg that has the same horizontal cross section as the steel cube. What is the magnitude of the "normal" force that the steel cube exerts on the load?
By how much does the steel cube compress, due to the load that it supports? (Give your answer as a positive number.)
To find the magnitude of the "normal" force that the steel cube exerts on the load, we can use Newton's third law, which states that for every action, there is an equal and opposite reaction.
In this case, the load exerts a downward force on the steel cube due to the force of gravity acting on it. As a reaction, the steel cube exerts an equal and opposite upward force on the load, known as the normal force.
To calculate the magnitude of the normal force, we need to determine the weight of the load, which is equal to the mass of the load multiplied by the acceleration due to gravity.
Given:
- Load mass = 85 kg
- Acceleration due to gravity = 9.8 m/s²
Weight = mass × acceleration due to gravity
Weight = 85 kg × 9.8 m/s² = 833 N
Therefore, the magnitude of the normal force that the steel cube exerts on the load is 833 N.
Now, let's calculate the compression of the steel cube due to the load. When a load is applied to a material, it can cause deformation or compression.
To find the compression, we need to use Hooke's Law, which states that the amount of deformation or compression of a material is directly proportional to the force applied.
Hooke's Law equation:
Stress = Young's Modulus × Strain
Where:
- Stress is the force applied per unit area
- Young's Modulus is the stiffness of the material
- Strain is the extent of deformation or compression
Given:
- Young's Modulus for steel = 2.0 × 10^11 N/m²
- Side length of the steel cube = 25 cm = 0.25 m
To calculate strain (deformation), we need to find the change in length from the original length of the steel cube when the load is applied.
Strain = Change in length / Original length
Change in length can be calculated using the equation:
Change in length = Stress / (Young's Modulus × Original cross-sectional area)
The original length of the steel cube is 0.25 m since it is a cube with sides of 0.25 m.
The original cross-sectional area can be calculated by squaring the side length:
Original cross-sectional area = (Side length)^2
Let's calculate the original cross-sectional area and change in length:
Original cross-sectional area = (0.25 m)^2 = 0.0625 m²
Change in length = (Weight of the load) / (Young's Modulus × Original cross-sectional area)
Change in length = 833 N / (2.0 × 10^11 N/m² × 0.0625 m²)
Now we can compare the values to check if there is a significant compression.
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For further assistance from me, more effort on your part will have to be shown.