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.
ScanSolve AI Answer
Here are the solutions to the problems: 1.2 Determine (1) the horizontal component and (2) the vertical component of a force that is exerted by the spring balance on the rubber band. Use a scale where 1 cm = 1 N. From the previous problem, we have: Magnitude of the force, F = 35 N Angle to the horizontal axis, = 30° The horizontal component (F_x) is given by F . The vertical component (F_y) is given by F . Step 1: Calculate the horizontal component. F_x = F F_x = 35 N × (30°) F_x = 35 N × sqrt(3)2 F_x ≈ 35 N × 0.8660 F_x ≈ 30.31 N Step 2: Calculate the vertical component. F_y = F F_y = 35 N × (30°) F_y = 35 N × (1)/(2) F_y = 17.5 N (1) Horizontal component: 30.31 N (2) Vertical component: 17.5 N 1.3 By keeping the reading on the spring balance the same, how will the magnitude of the horizontal component of the force change if the angle measured in the figure: The force F = 35 N remains constant. The horizontal component is F_x = F . 1.3.1 is increased to 60°? Step 1: Calculate the new horizontal component. F_x = 35 N × (60°) F_x = 35 N × 0.5 F_x = 17.5 N Step 2: Compare with the original horizontal component (30.31 N). The horizontal component will decrease from 30.31 N to 17.5 N. 1.3.2 is increased to 90°? Step 1: Calculate the new horizontal component. F_x = 35 N × (90°) F_x = 35 N × 0 F_x = 0 N Step 2: Compare with the original horizontal component (30.31 N). The horizontal component will decrease to 0 N. 1.4 When will the vertical component of the force that is read off the spring balance have a magnitude of 0 N? The vertical component is F_y = F . We want F_y = 0 N. F = 0 N Since the force F read off the spring balance is 35 N (which is not zero), then must be zero. = 0 This occurs when the angle is 0° (or 180°, etc.). In the context of an angle with the horizontal, this means the force is applied purely horizontally. The vertical component will have a magnitude of 0 N when the angle to the horizontal axis is 0°.