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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Here are the solutions to the physics problems: Question 25: We need to find the tension in the cable suspending the elevator. Step 1: Identify the forces acting on the elevator. The weight of the elevator acts downwards, and the tension in the cable acts upwards. Since the elevator is accelerating downwards, the net force is downwards. The net force is given by Newton's second law: F_net = ma. The forces are: Weight (W) = mg (downwards) Tension (T) (upwards) Since the acceleration (a) is downwards, the equation of motion is: W - T = ma Step 2: Rearrange the equation to solve for tension (T). T = W - ma T = mg - ma T = m(g - a) Step 3: Substitute the given values: mass (m = 1000 \, kg), acceleration due to gravity (g = 10 \, m/s^2), and elevator's acceleration (a = 1.0 \, m/s^2). T = 1000 \, kg × (10 \, m/s^2 - 1.0 \, m/s^2) T = 1000 \, kg × 9.0 \, m/s^2 T = 9000 \, N The tension in the cable is C. 9,000 \, N. Question 26: We need to calculate the peak voltage of an AC mains supply given its RMS value. Step 1: Recall the relationship between RMS voltage (V_rms) and peak voltage (V_p) for a sinusoidal AC supply. V_rms = (V_p)/(sqrt(2)) Step 2: Rearrange the formula to solve for peak voltage (V_p). V_p = V_rms × sqrt(2) Step 3: Substitute the given RMS voltage (V_rms = 220 \, V). V_p = 220 \, V × sqrt(2) V_p ≈ 220 \, V × 1.4142 V_p ≈ 311.124 \, V Rounding to the nearest whole number, the peak voltage is 311 \, V. The peak voltage is D. 311 \, V. Question 30: We need to find the resistance of the rheostat required to achieve a specific current. Step 1: Identify the components and their values. The circuit consists of a battery (V = 3.0 \, V), a fixed resistor (R_1 = 5 \, ), and a rheostat (R_rheostat). The desired current is I = 0.25 \, A. The internal resistance of the battery is negligible. Step 2: Since the components are in series, the total resistance (R_total) is the sum of the individual resistances. R_total = R_1 + R_rheostat Step 3: Use Ohm's Law to find the total resistance required for the given voltage and current. V = I × R_total R_total = (V)/(I) Step 4: Substitute the values for voltage and current. R_total = 3.0 \, V0.25 \, A R_total = 12 \, Step 5: Now, calculate the resistance of the rheostat. R_rheostat = R_total - R_1 R_rheostat = 12 \, - 5 \, R_rheostat = 7 \, The resistance of the rheostat must be adjusted to B. 7 \, . 3 done, 2 left today. You're making progress.