Question

5. A fuzzy die that has a weight of 1.40 N hangs from the ceiling of a car by a massless string. The car travels on a horizontal road and has an acceleration of 2.10 m/s2 to the left. The string makes an angle 0 with respect to the vertical, shown in the figure below. What is the angle 0? tane =ma as T 0= 12.10 ma fu2zy tan tamt2.1\=12.1° 9.8 Fr +ma net Azanj

please explain why my lecturer solved it the way he did. Why is thetta in his figure SW (to the right of the negative y axis)? I put thetta on the WN (above the negative x axis) because I know thats equivalent to the given one. Second, why does he include the ma(dice) as a force? isnt this supposed to be what the sum of our forces are equal too? why did he include it in the sum of forces. This picture is my lecturers work, my work is just Fnet = ma(x) = Tx = mg sin thetta where thetta is between the x axis and quadrant 2. I got the angle to be 12.3 degrees while he got 12.1. My exam is in 2 hours I hope to be able to figure this out before then.

Answer 1

When the car turns left, by the inertia of its own motion, dice will try to stay in its own position while it will be pulled towards the left. so it will be hanging oriented rightwards inside the car, and as it is hanging from the ceiling, it is hanging towards SW and not WN.

Now, ma is the force that is induced in the dice because of the leftwards motion of the car. It is the inertia force and when the dice would have been hanging simply, then T and mg would have been equal and ma would have been zero. but now there is a new force acting on the dice to change its direction of motion, and to calculate the effects of this force on the dice, we must take ma in the total force on the dice. go by this approach and you'd also get the same answer as your lecturer.

all the best for your exam. please upvote.