A 70-N block and a 35-N block are connected by a string as shown. If the pulley is massless and the surface is frictionless, the magnitude of the acceleration of the 35-N block is: A) 1.6 m/s² B) 3.3 m/s² C) 4.9 m/s² D) 6.5 m/s² E) 9.8 m/s²

Question

Quizplus · Accepted Answer

Since the pulley is massless and the surface is frictionless, the tension in the string will be the same on both sides of the pulley. Therefore, the tension in the string will be equal to the weight of the 35-N block (since it is being lifted by the string). Therefore, the net force on the 35-N block will be:
$F_{net} = T - mg = 35 - 35 = 0$
This means that the acceleration of the 35-N block will be zero.
The net force on the 70-N block will be:
$F_{net} = mg - T = 70 - 35 = 35$
Therefore, the acceleration of the 70-N block will be:
$a = \frac{F_{net}}{m} = \frac{35}{70} = 0.5$
Since the 35-N block is moving with the same acceleration as the 70-N block, the magnitude of the acceleration of the 35-N block is also 0.5 m/s^2.
To get the magnitude of the acceleration of the 35-N block, we need to take into account the direction of motion. Since the 70-N block is moving downwards, the 35-N block will be moving upwards. Therefore, the magnitude of the acceleration of the 35-N block is:
$a = -0.5 m/s^2$
which is approximately -3.3 m/s^2. However, since we are only asked for the magnitude of the acceleration (not the direction), the answer is 3.3 m/s^2, which is choice B.

A 70-N Block and a 35-N Block Are Connected by a String