Answer to Question #145830 in Mechanics | Relativity for Bre

Question

imagine that one cart is oriented perfectly in-line with the string, but the other cart is skewed so that there is an angle, θ, between the direction that the string

was pulling and the direction the force sensor can measure.

Choose the pair of force measurements with the largest difference and determine the associated angle θ of the cart. Neglect uncertainty here.

The forces measured are 43.48 N and 42.60 N

Answer 1

Explanations & Calculations

• To make some sense of the situation, an assumption can be made as follows & refer to the figure attached.

• The thread is pulling both the carts same time with a fixed tension at the moment & the force sensors are set up on each cart which measure forces act perpendicular to a cart. Therefore, the blue cart measures the force imposed on it by the thread which is exactly its tension, as the cart (the force sensor more precisely) is in-line with the thread while the green one measures only the tension's component perpendicular to it (along the dotted blue line).
• As both the carts start to move blue one continues straight with the thread while the green one adjusts its orientation to an in-line position before moving which gradually reduces the difference between the measurements from the sensors of the 2 carts.
• Therefore, it is vital to get the very first measurements from the carts accurately as possible.
• Since the thread connected to both carts is the same one, tension in it is the same through it (red line :"T")

• Therefore, blue cart measures the actual tension (43.48N) while the green one measuring only a component of it (42.60N)
• Therefore, considering the resolution of the tension along the perpendicular,

$\qquad\qquad \begin{aligned} \small 42.60N &= \small 43.48 \cos\theta\\ \small \cos\theta &= \small \frac{42.60}{43.48}\\ \small \theta &= \small \bold{11.547^0} \end{aligned}$

• Hope this helps.