Textbook Question
(a) What minimum force F is needed to lift a piano (mass M) using the pulley apparatus shown in Fig. 4–64?
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6. Intro to Forces (Dynamics)
Forces in Connected Systems of Objects
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Block 1 has a mass of 7 kg and Block 2 has a mass of 3 kg, and they are connected to each other by a rope. A 40 N force is applied to Block 2. What is the tension in the rope between Blocks 1 and 2?
A
30 N
B
28 N
C
40 N
D
10 N
Verified step by step guidance1
Identify the system: We have two blocks connected by a rope, with a force applied to Block 2. The goal is to find the tension in the rope between the blocks.
Calculate the acceleration of the system: Since both blocks are connected, they will have the same acceleration. Use Newton's second law, \( F = ma \), where \( F \) is the total force applied to the system, \( m \) is the total mass, and \( a \) is the acceleration. The total mass is the sum of the masses of Block 1 and Block 2.
Determine the net force acting on the system: The force applied to Block 2 is 40 N. Since there is no friction mentioned, this is the net force acting on the system.
Calculate the acceleration: Use the formula \( a = \frac{F}{m} \), where \( F \) is the net force (40 N) and \( m \) is the total mass (7 kg + 3 kg).
Find the tension in the rope: Consider only Block 1. The tension in the rope is the force that accelerates Block 1. Use \( T = m_1 \cdot a \), where \( T \) is the tension, \( m_1 \) is the mass of Block 1, and \( a \) is the acceleration calculated in the previous step.
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