(Solved): A rope is loosely fastened, (i.e. it can swing back and forth) to the ceiling of a railway car. Wh ...

A rope is loosely fastened, (i.e. it can swing back and forth) to the ceiling of a railway car. When a block of unknown mass is hung from the rope and the car maintains a constant acceleration, the rope is oriented at an angle of \( 6^{\circ} \) as shown in the figure. All of the following questions refer to the time when the car is accelerating and the rope is maintaining a constant angle with respect to the vertical. (a) What must the direction of the acceleration of the car be? Explain. (b) What is the direction of the velocity? Explain. (c) Find the acceleration of the railway car (hint: find a symbolic expression for the magnitude of the acceleration before plugging in numbers) (hint 2: when you don't know what the value of a quantity is, give it a name / variable). (d) Use the Proportionality sense-making technique to check your symbolic expression for the acceleration in part (c). Does the acceleration increase or decrease as the angle increases? Explain what you would expect the relationship between acceleration and angle to be and why, then compare to the relationship your expression shows.