Two blocks of masses 2 kg and 3 kg are connected by a light string over a frictionless pulley. If the 3 kg block is released from rest, what is the acceleration of the system?
Practice Questions
1 question
Q1
Two blocks of masses 2 kg and 3 kg are connected by a light string over a frictionless pulley. If the 3 kg block is released from rest, what is the acceleration of the system?
1.2 m/s²
2 m/s²
3 m/s²
4 m/s²
Using Newton's second law, the net force is (3 kg - 2 kg) * g = 1 kg * 9.8 m/s². The total mass is 5 kg, so a = F/m = 9.8 N / 5 kg = 1.96 m/s², approximately 2 m/s².
Questions & Step-by-step Solutions
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Q
Q: Two blocks of masses 2 kg and 3 kg are connected by a light string over a frictionless pulley. If the 3 kg block is released from rest, what is the acceleration of the system?
Solution: Using Newton's second law, the net force is (3 kg - 2 kg) * g = 1 kg * 9.8 m/s². The total mass is 5 kg, so a = F/m = 9.8 N / 5 kg = 1.96 m/s², approximately 2 m/s².
Steps: 8
Step 1: Identify the masses of the two blocks. The first block has a mass of 2 kg and the second block has a mass of 3 kg.
Step 2: Understand that the 3 kg block will fall down due to gravity when released, causing the 2 kg block to move up.
Step 3: Calculate the gravitational force acting on each block. The force on the 3 kg block is 3 kg * g (where g = 9.8 m/s²), which equals 29.4 N.
Step 4: Calculate the gravitational force acting on the 2 kg block. The force on the 2 kg block is 2 kg * g, which equals 19.6 N.
Step 5: Determine the net force acting on the system. The net force is the difference between the force on the 3 kg block and the force on the 2 kg block: 29.4 N - 19.6 N = 9.8 N.
Step 6: Calculate the total mass of the system. The total mass is 2 kg + 3 kg = 5 kg.
Step 7: Use Newton's second law (F = ma) to find the acceleration. Rearranging gives a = F/m. Substitute the net force (9.8 N) and total mass (5 kg) into the equation: a = 9.8 N / 5 kg.
Step 8: Calculate the acceleration: a = 1.96 m/s², which can be approximated to 2 m/s².
