A brass rod is 185 cm long and 1.60 cm in diameter. What force must be applied to each end of th

A brass rod is 185 cm long and 1.60 cm in diameter. What...

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Key Concepts

Thermal Stress

Thermal stress occurs when a material undergoes a change in temperature but its expansion or contraction is restricted. This constraint creates internal stress as the material tries to expand or contract but is held fixed. Understanding thermal stress is critical in designing systems that need to withstand temperature fluctuations without experiencing structural failure.

Young's Modulus

Young's Modulus is a measure of a material's stiffness, defined as the ratio of stress to strain in the linear elastic region of the material's behavior. It is used to calculate the stresses produced in a material when it is deformed and is essential for determining the force needed to counteract temperature-induced changes when the material is mechanically restrained.

Thermal Expansion

Thermal expansion refers to the tendency of a material to change its dimensions in response to a change in temperature. When a material is heated, it tends to expand; when cooled, it contracts. This concept is crucial for understanding how temperature variations lead to dimensional changes in materials and how coefficients of thermal expansion quantify those changes.

Transcript

00:01 On this problem, we're presented with a brass rod of a certain length and diameter.

00:07 It goes through a temperature change, and we're asked what forces needed to keep the bar contracting.

00:15 So this is a thermal stress problem, and our relevant equation is force over a cross -sectional area equals the opposite of young's modulus for whatever material times the coefficient of linear.

00:32 Expansion times change in temperature.

00:37 So let's make sure this is the equation for us.

00:41 We have force.

00:44 That's what we're looking for.

00:45 So it better be in the equation.

00:48 Cross -sectional area.

00:51 We're not given this, but we're given the diameter.

00:53 So we can easily find that.

00:57 Young's modulus.

00:59 That's based on the material.

01:01 We're told it's a brass rod.

01:03 So we can, or you can, look up the youngs modulus in a table in your physics textbook.