Question

Two blocks are connected by a string and pulley . Assuming that the string and pulley are massless, the magnitude of the acceleration of each block is:

A) 5 m/s²
B) 10 m/s²
C) 2 m/s²
D) 20 m/s²

Answer 1

In a system where two blocks are connected by a massless rope and pulley, the magnitude of the acceleration of each block is the same. The formula to calculate the acceleration is (m2 - m1) / (m1 + m2), where m1 and m2 are the masses of the two blocks.

Step-by-step explanation:

In a system where two blocks are connected by a massless rope and pulley, assuming no friction, the magnitude of the acceleration of each block is the same. Let's call this acceleration 'a'.

The equation to calculate the acceleration for each block is given by:

a = (m2 - m1) / (m1 + m2)

where m1 and m2 are the masses of the two blocks. In this specific problem, we are given the masses: m1 = 4.0 kg and m2 = 1.0 kg. Plugging in these values into the equation: a = (1.0 kg - 4.0 kg) / (4.0 kg + 1.0 kg) = -3.0 kg / 5.0 kg = -0.6 m/s².

Since acceleration cannot be negative in this context, we take the magnitude of the acceleration: |a| = 0.6 m/s². Therefore, the correct answer is:

Option C) 2 m/s²