An electric motor is a device that utilizes the magnetic effect of electric current. When a current-carrying coil is placed in a magnetic field, it experiences a force (Fleming's Left-Hand Rule) that causes it to rotate. Therefore, it continuously converts electrical energy into mechanical energy. A generator does the reverse.
An engine pumps water continuously through a hose. Water leaves the hose with a velocity 'v' and mass per unit length is 'm'. What is the power imparted to the water?
Explanation:
Power is the rate of doing work or imparting kinetic energy (dK/dt). Mass exiting per second = m * v (mass/length * length/time). Kinetic energy imparted per second = 1/2 * (mass per second) * v^2 = 1/2 * (mv) * v^2 = 1/2 * m * v^3. This is a very common advanced mechanics question.
Explanation:
Orbital velocity v = √(GM/r), where r is orbital radius from Earth's center. Thus v ∝ 1/√r. If r increases, v decreases. This follows from equating gravitational force to centripetal force: GMm/r² = mv²/r ⇒ v = √(GM/r). Higher orbits have slower speeds but longer periods. Memory aid: 'Higher orbit, slower speed' – counterintuitive but fundamental. This relationship is crucial for satellite motion questions in competitive exams. Always distinguish orbital velocity from escape velocity (which is √2 times orbital velocity at same radius).
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