This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify the forces and their components. The block has a mass m = 3 kg. There are two applied forces: • A horizontal force F_1 = 12 N to the left. • A force F_2 = 30 N at an angle of 60^ above the horizontal, pointing to the right. We need to resolve F_2 into its horizontal (F_2x) and vertical (F_2y) components: F_2x = F_2 (60^) = 30 N × 0.5 = 15 N (to the right) F_2y = F_2 (60^) = 30 N × sqrt(3)2 ≈ 30 N × 0.866 = 25.98 N (upwards) Step 2: Calculate the net horizontal force ( F_x). Let's consider the right direction as positive. F_x = F_2x - F_1 = 15 N - 12 N = 3 N The net horizontal force is 3 N to the right. Since this is not zero, the block will accelerate horizontally. Step 3: Calculate the net vertical force ( F_y) to check if the block lifts off. The gravitational force acting on the block is F_g = mg. F_g = 3 kg × 9.8 m/s^2 = 29.4 N (downwards) The upward component of the applied force is F_2y = 25.98 N. To lift off the floor, the total upward force must be greater than the gravitational force. In this case, F_2y < F_g (25.98 N < 29.4 N). Therefore, the block will not lift off the floor. There will be a normal force from the surface supporting the block. Step 4: Determine the block's motion. Since there is a net horizontal force of 3 N to the right, and the block does not lift off the floor, the block will accelerate to the right. The final answer is C. accelerate to the right. Send me the next one 📸