Question

Two blocks are positioned on surfaces, each inclined at the same angle of 51.3 degrees with respect to the horizontal. The blocks are connected by a rope which rests on a frictionless pulley at the top of the inclines as shown, so the blocks can slide together. The mass of the black block is 5.92 kg, and the coefficient of kinetic friction for both blocks and inclines is 0.550. Assume static friction has been overcome and that everything can slide. What is must be the mass of the white block if both blocks are to slide to the LEFT at an acceleration of 1.5 m/s²? a) 3.45 kg b) 4.42 kg c) 26.66 kg d) 14.48 kg

Answer 1

To find the mass of the white block, we can use Newton's second law and set up an equation with the forces involved. Solving for the mass of the white block gives us an answer of approximately 8.42 kg.

Step-by-step explanation:

To find the mass of the white block, we can use Newton's second law, which states that the net force is equal to the mass times the acceleration. In this case, the net force is the force due to gravity pulling the black block down the incline, minus the force of kinetic friction pulling the black block up the incline. The force due to gravity can be calculated as the mass times the acceleration due to gravity. The force of kinetic friction can be calculated as the coefficient of kinetic friction times the normal force.

Since the blocks are connected by a rope, they will have the same acceleration. Therefore, the net force on the white block will be equal to its mass times the acceleration. Setting up the equation and solving for the mass of the white block: Net Force = (Mass of White Block) * (Acceleration) =

(Mass of Black Block) * (Acceleration due to Gravity) - (Coefficient of Kinetic Friction) * (Normal Force) = (Mass of White Block) * (Acceleration) = (5.92 kg) * (9.8 m/s²) - (0.550) * [(Mass of White Block) * (9.8 m/s²)] = (Mass of White Block) * (1.5 m/s²) Simplifying the equation: 58.016 - (5.39)(Mass of White Block) = (1.5)(Mass of White Block) Combining like terms: 6.89(Mass of White Block) = 58.016

Solving for the mass of the white block: (Mass of White Block) = 58.016/6.89 = 8.42 kg

Therefore, the mass of the white block must be approximately 8.42 kg.

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