Question

2. Two masses are connected by a light string over a light, frictionless pulley, as in Fig. 7 - 1 . The table surface is also frictionless. (a) Apply the work-energy theorem for this system to calculate the speed of the masses after the masses have moved a distance delta*x starting from rest. Note that the work of the ten- sions drops out. (b) Use this result to obtain the acceleration of the system.

Answer 1

(a) v = sqrt((2g / (m1/m2 + 1)) * Δx), where m1 and m2 are masses, g is acceleration due to gravity.

(b) a = 2g / (m1/m2 + 1).

In the given system with two masses connected by a light string over a frictionless pulley and a frictionless table surface, the work-energy theorem can be applied to determine the speed and acceleration.

(a) Applying the work-energy theorem, the speed (v) of the masses after moving a distance Δx starting from rest is given by v = sqrt((2g / (m1/m2 + 1)) * Δx), where
`m_1`​ and
`m_2` represent the masses, and g is the acceleration due to gravity. It's important to note that the work of the tensions in the system drops out from the calculation.

(b) Utilizing the result from part (a), the acceleration (a) of the system can be determined as a = 2g / (m1/m2 + 1). This expression provides the acceleration of the masses in the system, considering the masses' relationship and the influence of gravity. The outcomes of these calculations offer insights into the dynamic behavior of the masses as they move a given distance under the specified conditions.