Question

Three identical blocks connected by ideal (massless) strings are being pulled along a horizontal frictionless surface by a horizontal force F⃗ . The magnitude of the tension in the string between blocks B and C is T. Assume that each block has mass m

A) What is the magnitude F of the force?
Express your answer in terms of given quantities.
B) What is the tension TAB in the string between block A and block B?
Express your answer in terms of given quantities.

Answer 1

A) Magnitude of the force F:

The tension in the string between blocks B and C is the same as the net force acting on block B. The net force acting on block B is equal to the sum of the forces acting on it. These forces are the tension in the string between blocks A and B, the tension in the string between blocks B and C, and the gravitational force acting on block B. The magnitude of the net force acting on block B is given by the following equation:

F = TAB + T + m * g

where:

F = magnitude of the force

TAB = tension in the string between blocks A and B

T = tension in the string between blocks B and C

m = mass of each block

g = acceleration due to gravity (9.8 m/s^2)

Setting TAB + T = F, we have:

F = T + m * g

Rearranging the equation, we get:

T = (F - m * g)

So, the magnitude of the force F is given by:

F = T + m * g

B) Tension TAB in the string between blocks A and B:

Since the system is in equilibrium, the net force acting on block A must be equal to zero. The net force acting on block A is equal to the sum of the forces acting on it. These forces are the tension in the string between blocks A and B and the gravitational force acting on block A. The magnitude of the net force acting on block A is given by the following equation:

0 = TAB - m * g

Solving for TAB, we have:

TAB = m * g