Question

Two blocks connected by a rope of negligible mass are being dragged by a horizontal force f. Suppose that f = 56.0N, m1 = 13.5kg, m² = 12.5kg, and the coefficient of kinetic friction between each block and the surface is 0.107. Determine the tension t, rounded to one decimal place. Use g = 9.8m/s².

Answer 1

To find the tension in the rope, consider the forces on the blocks, calculate net forces, use Newton's second law to find acceleration, and then use the acceleration to determine the tension.

Step-by-step explanation:

To find the tension in the rope, we need to consider the forces acting on the blocks. The horizontal force F is responsible for accelerating the blocks, while the kinetic friction between the blocks and the surface opposes this motion.

First, calculate the net force acting on each block. For the block on the table, the net force is the difference between the applied force F and the frictional force, which is equal to the coefficient of kinetic friction (μ) multiplied by the normal force. For the hanging block, the net force is the difference between the tension in the rope and the weight of the block.

Using the net forces, apply Newton's second law (F = ma) to find the acceleration of each block. Since the blocks are connected by a rope, they will have the same acceleration. Finally, use the acceleration to determine the tension in the rope using the equation T = (m1 + m2)a.