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 given forces and the scale. We have two forces acting at a right angle: F_1 = 30 N F_2 = 40 N The given scale for drawing is 1 cm = 5 N. Step 2: Convert the forces to lengths for the scale drawing. To represent F_1 = 30 N on the drawing: Length_1 = 30 N5 N/cm = 6 cm To represent F_2 = 40 N on the drawing: Length_2 = 40 N5 N/cm = 8 cm Step 3: Explain the graphical method for determining the resultant force. Draw the first force vector (F_1) as a line segment 6 cm long. Let's assume it acts horizontally. From the head (end) of the first vector, draw the second force vector (F_2) as a line segment 8 cm long, perpendicular to the first vector (since they act at a right angle). The resultant force vector (R) is drawn from the tail (start) of the first vector to the head of the second vector. Measure the length of this resultant vector (R) with a ruler. Convert this length back to Newtons using the scale (1 cm = 5 N). Measure the angle () the resultant vector makes with the first force vector using a protractor. This angle represents the direction. Step 4: Calculate the magnitude of the resultant force analytically (as a scale drawing should yield this result). Since the forces are at a right angle, we can use the Pythagorean theorem: R = sqrt(F_1^2 + F_2^2) Substitute the force values: R = sqrt((30 N))^2 + (40 N)^2 R = sqrt(900 N)^2 + 1600 N^2 R = sqrt(2500 N)^2 R = 50 N Step 5: Calculate the direction of the resultant force analytically. The direction can be found using the tangent function, where is the angle the resultant makes with the 30 N force: = OppositeAdjacent = (F_2)/(F_1) = 40 N30 N = (4)/(3) = ((4)/(3)) ≈ 53.13^ The magnitude of the resultant force is 50 N. The direction of the resultant force is 53.13^ from the 30 N force. Got more? Send 'em.