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Chapter 3: Problem 148

Three identical blocks of masses \(m=2 \mathrm{~kg}\) each are drawn by a force \(F=10.2 \mathrm{~N}\) with an acceleration of \(0.6 \mathrm{~m} / \mathrm{s}^{2}\) on a surface, then what is the tension (in N) in the string between \(B\) and \(C\), if there is no friction between the surface and the blocks \(A\) and \(B\) (A) \(9.2\) (B) \(3.4\) (C) 4 (D) \(9.8\)

Short Answer

Expert verified
The tension between blocks B and C is approximately 3.6 N, which is closest to option (B) \(3.4\).

Step by step solution

01

Identify the forces and their directions

There are two main forces acting on the system: 1. Applied force (F): 10.2 N to the right 2. Tension force (T) between blocks B and C, also acting to the right since there is no friction between blocks A and B
02

Calculate the total mass of the system

The masses of each block are identical (2 kg). Thus, the total mass (M) of the system can be calculated as: M = m1 + m2 + m3 = 2 kg + 2 kg + 2 kg = 6 kg
03

Identify the Newton's second law of motion formula

Newton's second law of motion states that the force applied to an object is equal to the mass of the object multiplied by its acceleration: F = M * a
04

Solve for the Force on block C

We are looking for the force applied to block C, which we will call F_c. Since there is no friction between blocks A and B, the force applied to block A is the same as the force applied to block C. Using the information given and Newton's second law of motion, we can solve for F_c: F = M * a 10.2 N = 6 kg * 0.6 m/s^2 F_c = 3.6 N
05

Calculate the tension (in N) between blocks B and C

The tension between blocks B and C will be the same as the force on block C, F_c, because there is no friction between blocks A and B. Thus, tension = F_c Tension = 3.6 N The correct answer is approximately 3.6 N, which is closest to option (B) \(3.4\).

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