Potencia necesaria para subir pendiente a cierta velodidad

In this physics problem, we calculate the mechanical power developed by a man climbing an inclined plane at a constant speed. The solution will help us understand how the dot product of force and velocity is used and why only the vertical component of velocity is involved. Instantaneous mechanical power can be expressed as the dot product: P = F · v Since the force opposing weight is vertical, we must decompose the man's velocity into its horizontal and vertical components. The component involved in calculating power is: vy = v · sin 10° Thus: P = mgvy and, therefore: P = mgv · sin 10° STATEMENT An 80 kg man climbs a plane inclined at 10° to the horizontal at a constant speed of 6 km/h. Calculate the power he develops. During the solution, we converted the speed from kilometers per hour to meters per second, analyzed the force and velocity vectorially, expanded the dot product, and calculated the vertical component of the motion. Keeping enough decimal places, the power obtained is approximately 227 W. Using the rounded intermediate values ​​employed throughout the video, the result is approximately 228 W. CHAPTERS 00:00 Power Problem on an Inclined Plane 00:20 Power Developed by a Man 00:25 Formula for Mechanical Power 00:52 Representation of the Inclined Plane 01:02 The Man Must Overcome His Weight 01:18 Force Required to Climb at a Constant Speed 01:50 Direction of Force and Velocity 02:02 Decomposition of Velocity into Components 02:32 Vector Formulation of the Problem 02:47 Dot Product of Force and Velocity 03:17 Complete Expansion of the Dot Product 03:45 Dot Product of Perpendicular Vectors 03:59 Dot Product of Equal Unit Vectors 04:14 Component that Determines Power 04:46 Values ​​of F and y vy 05:09 Relationship between angles 05:57 Vertical component of velocity 06:21 Formula P = mgv · sin 10° 07:00 Substituting the data 07:26 Converting 6 km/h to m/s 08:17 Calculating sin 10° 08:52 Units of power 09:01 Final operations 09:26 Result: approximately 228 W 09:39 Interpreting the result More lessons on mechanical work here:    • Trabajo mecánico   #MechanicalPower #InclinedPlane #PhysicsWithJuan