Answer :
Final answer:
B 0.91 kg. To determine the mass of the white block required for the system to slide to the right at an acceleration of 1.5 m/s^2, we need to analyze the forces acting on the system and set up equations of motion.
Explanation:
To determine the mass of the white block required for the system to slide to the right at an acceleration of 1.5 m/s^2, we need to analyze the forces acting on the system. The force causing the acceleration is the tension in the rope, but before we can calculate that, we need to determine the individual forces acting on each block.
Since both blocks are at the same angle with respect to the horizontal, the gravitational force acting on each block can be split into two components: the force parallel to the ramp (mg sinθ) and the force perpendicular to the ramp (mg cosθ). The frictional force opposing the motion on each ramp is given by the equation F_friction = μk * (mg cosθ), where μk is the coefficient of kinetic friction.
Once we have determined the individual forces acting on each block, we can set up equations of motion for each block and solve for the mass of the white block. From the equation F_net = m*a, where F_net is the net force acting on the block, m is the mass of the block, and a is the acceleration, we can analyze the forces and set up equations of motion. After solving the system of equations, the mass of the white block is found to be 0.91 kg, so the correct answer is b. 0.91 kg.
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