Question

2. PLEASE READ THE INSTRUCTIONS CAREFULLY. DRAW SKETCH AND DIAGRAM AND FREE-BODY DIAGRAM, LIST KNOWNS AND UNKNOWNS PLEASE.

Problem Statement

Three boxes in contact rest side-by-side on a smooth, horizontal floor. Their masses are 5.0-kg, 3.0-kg, and 2.0-kg, with the 3.0-kg box in the center. A force of 50 N pushes on the 5.0-kg box, which pushes against the other two boxes. a. What magnitude force does the 3.0-kg box exert on the 5.0-kg box? b. What magnitude force does the 3.0-kg box exert on the 2.0-kg box?

Visual Representation

• Draw a sketch of the problem

• Identify “the system” by circling the object(s) of interest

• Establish a coordinate system and define symbols

• Draw a motion diagram for “the system” and determine

• Make a free-body diagram showing all the forces acting on “the system”

• List knowns and desired unknowns Mathematical Representation

• Write down Newton’s second law in component form

• Use the free-body diagram to obtain the force components for Newton’s laws

• Solve equation(s) for the desired unknown

• Substitute in the known values, including units, and calculate unknown value

• Check units and assess if your answer is reasonable

Answer 1

Solution :

Given :

m₁ = 5 kg

m₂ = 3 kg

m₃ = 2 kg

And, F_push = 50 N

According to Newton's Second law : F_net = F_x = m a

∴ F_push = (m₁ + m₂ + m₃) a

∴ (50 N) = (5 kg + 3 kg + 2 kg) a

∴ a = 5 m/s²

Therefore, Acceleration of the system will be 5 m/s².

.

And, According to the Newton's third law of motion :

The force exerted by 3 kg box on the 5 kg box (F₁₂) will be equal to the force exerted by 5 kg box on 3 kg box (F₂₁).

Here, F₂₁ = (m₂ + m₃) a = (3 kg + 2 kg)(5 m/s²) = 25 N

Therefore : The force exerted by 3 kg box on the 5 kg box will be 25 N.

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Similarly, Force exerted by the 3 kg box on 2 kg box will be : F₃₂ = m₃ a = (2 kg)(5 m/s²) = 10 N