Here are the solutions to the questions: 46. Two forces, $F_1$ and $F_2$, are applied on a crate lying on a frictionless, horizontal surface. $F_1$ is directed towards the west (left) and $F_2$ is directed towards the east (right). The problem states that the magnitude of force $F_1$ is greater than that of force $F_2$. Since the surface is frictionless, the net force on the crate determines its motion. The net force $F_{net}$ will be in the direction of the larger force. Given $F_1 > F_2$, the net force will be in the direction of $F_1$, which is towards the west. According to Newton's Second Law, a net force causes acceleration. Therefore, the crate will accelerate towards the west. The correct option is B. B) accelerate towards the west. 47. The speed of a bicycle increases from $2 \text{ m}\cdot\text{s}^{-1}$ to $8 \text{ m}\cdot\text{s}^{-1}$. We need to find the factor by which its kinetic energy increases. The formula for kinetic energy is $E_k = \frac{1}{2}mv^2$. Step 1: Calculate the initial kinetic energy ($E_{k1}$). $$E_{k1} = \frac{1}{2}m(v_1)^2$$ $$E_{k1} = \frac{1}{2}m(2 \text{ m}\cdot\text{s}^{-1})^2$$ $$E_{k1} = \frac{1}{2}m(4 \text{ m}^2\cdot\text{s}^{-2})$$ $$E_{k1} = 2m$$ Step 2: Calculate the final kinetic energy ($E_{k2}$). $$E_{k2} = \frac{1}{2}m(v_2)^2$$ $$E_{k2} = \frac{1}{2}m(8 \text{ m}\cdot\text{s}^{-1})^2$$ $$E_{k2} = \frac{1}{2}m(64 \text{ m}^2\cdot\text{s}^{-2})$$ $$E_{k2} = 32m$$ Step 3: Determine the factor of increase. The factor of increase is the ratio of the final kinetic energy to the initial kinetic energy. $$\text{Factor} = \frac{E_{k2}}{E_{k1}}$$ $$\text{Factor} = \frac{32m}{2m}$$ $$\text{Factor} = 16$$ The correct option is D. D) 16 48. The pressure versus time graphs represent sound waves. We need to identify the graph that best represents a sound wave with the highest frequency and the loudest sound. • Frequency is the number of cycles per unit time. A higher frequency means more oscillations (waves) occur within the same time interval. • Loudness is related to the amplitude of the sound wave. A louder sound corresponds to a larger amplitude, which means a greater variation in pressure from the equilibrium. Let's analyze the graphs: • Graph A shows many oscillations within the given time, indicating high frequency. It also shows the largest vertical displacement (amplitude), indicating a loud sound. • Graph B shows fewer oscillations than A (lower frequency) and a smaller amplitude than A (quieter sound). • Graph C shows the fewest oscillations (lowest frequency) and a smaller amplitude than A (quieter sound). • Graph D shows fewer oscillations than A (lower frequency) and a smaller amplitude than A (quieter sound). Comparing all options, Graph A has both the highest frequency (most waves in the given time) and the largest amplitude (loudest sound). The correct option is A. A) 3 done, 2 left today. You're making progress.