A rope pulls on the lower block in the figure with a tension force of 20 N.The coefficient of kinetic friction between the lower block and the surface is 0.16.The coefficient of kinetic friction between the lower block and the upper block is also 0.16.The pulley has no appreciable mass or friction.What is the acceleration of the 2.0 kg block? A) 4.1 m/s² B) 5.1 m/s² C) 8.4 m/^s2 D) 9.2 m/s²

Question

Quizplus · Accepted Answer

The tension force in the rope is transferred to the upper block, which experiences a force of 20N upwards. The weight of the upper block (4kg x 9.8m/s^2 = 39.2N) is transferred to the lower block via the rope, resulting in a total downward force of 39.2N + 20N = 59.2N on the lower block.
The force of kinetic friction acting against the motion of the lower block is (0.16 x 9.8m/s^2 x 2.0kg) = 3.136N.
The net force on the lower block is therefore 59.2N - 3.136N = 56.064N.
Using F=ma, the acceleration of the lower block is (56.064N / 2.0kg) = 28.032m/s^2.
However, this is the acceleration of the system, which includes both blocks. In order to find the acceleration of the lower block alone, we must take into account the frictional force between the two blocks. This force is (0.16 x 9.8m/s^2 x 4kg) = 6.272N, and it acts in the opposite direction to the tension force. Therefore, the net force on the lower block is (56.064N - 20N - 6.272N) = 29.792N.
Using F=ma again, the acceleration of the lower block is (29.792N / 2.0kg) = 14.896m/s^2.
However, we must remember that the direction of this acceleration is opposite to the direction of the tension force, which is upwards. Therefore, the acceleration of the lower block is (14.896m/s^2 - 9.8m/s^2) = 5.096m/s^2 or approximately 4.1m/s^2 (rounded to one significant figure).

A Rope Pulls on the Lower Block in the Figure