This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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b) Three examples of simple harmonic motion are: • The oscillation of a simple pendulum (for small angles). • The oscillation of a mass attached to a spring. • The vibration of a tuning fork. 2. Hooke's Law states that within the elastic limit, tensile stress is directly proportional to tensile strain. Mathematically, this is expressed as: = E where is the tensile stress, is the tensile strain, and E is Young's modulus (the constant of proportionality). 3. Step 1: Calculate the spring constant (k). Given: Natural length, L_0 = 3.4 m Extension, L_1 = 0.02 m Force, F_1 = 5 N Using Hooke's Law, F = k L: k = (F_1)/( L_1) k = 5 N0.02 m k = 250 N/m Step 2: Calculate the new extension ( L_2) when the applied force is 14 N. Given: New force, F_2 = 14 N Spring constant, k = 250 N/m Using Hooke's Law: L_2 = (F_2)/(k) L_2 = 14 N250 N/m L_2 = 0.056 m Step 3: Calculate the new total length (L_2). L_2 = L_0 + L_2 L_2 = 3.4 m + 0.056 m L_2 = 3.456 m The length of the spring when the applied force is 14 N will be 3.456 m. 4. Step 1: Identify the given values. Tensile stress, = 3.7 × 10^9 Nm^-2 Length increases by 7% of its original length. This means the tensile strain () is 7%. Step 2: Convert the percentage increase in length to tensile strain. Tensile strain, = change in lengthoriginal length If the length increases by 7%, then ( L)/(L_0) = 0.07. So, = 0.07. Step 3: Calculate Young's modulus (E). Young's modulus is defined as the ratio of tensile stress to tensile strain: E = ()/() E = 3.7 × 10^9 Nm^-20.07 E ≈ 5.2857 × 10^10 Nm^-2 Step 4: Round the result to an appropriate number of significant figures. E ≈ 5.29 × 10^10 Nm^-2 The Young's modulus of the wire is 5.29 × 10^10 Nm^-2.