Unit iv dynamics of particles
- 1. UNIT IV-DYNAMICS OF PARTICLES (2 marks) 1. State D`Alembert`s principle. D`Alembert`s principle says that when a rigid body is under motion, there will be an imaginary inertia force `ma`, that acts opposite to the motion to keep the system in dynamic equilibrium. 2. State the principle of work and energy. It states that “when a particle moves from S1 to S2 under the action of force F, the change in kinetic energy of the particle is equal to the work of the force F”. (Work done) x S1-2 =(KE)2 – (KE)1 (or) (KE)1 – (Work done) x S1-2 =(KE)2 3. State impulse momentum principle. The impulse of the force acting on particle is equal to the change in the linear momentum of the particle. Impulse = change in momentum = Final momentum (M1) – initial momentum (M2) (M1) + ∑F alongmotion x ∆t = (M2) 4. Define the term “collision of elastic bodies”. Impact means the collision of two bodies which occurs in a very small interval of time and during which the two bodies exert very large force on each other. 5. Define the co-efficient of restitution. The co-efficient of restitution between two bodies in a collision is defined as the ratio of the relative velocity of their separation after collision to the relative velocity of their approach before collision. It is denoted by `e`. e = (V2-V1) / (U1-U2) 6. What is impulsive force? When a large force acts on a body for a short period of time, then the force is called an impulsive force. Example 1. Cricket ball hit by a bat. 2. Football kicked by the player etc., 7. Distinguish between rectilinear and curvilinear motion. When a particle moves along a straight line, then it is called rectilinear motion or translation. Example: A car moving on a straight road When a particle moves in a curved path, then it is called curvilinear motion. Example: A rocket launched in space
- 2. 8. Define uniform rectilinear motion. If a particle moves on a straight line with constant velocity, then the particle is said to be in uniform rectilinear motion (URM). It is expressed as dx/dt = V = constant 9. Define uniformly accelerated/decelerated or retarded rectilinear motion (UARM/UDRM Or URRM) If a particle moves on a straight line with constant acceleration, then the particle is said to be in uniformly accelerated rectilinear motion. (UARM). If a particle moves on a straight line with constant deceleration/retardation, then the particle is said to be in uniformly accelerated rectilinear motion. (UDRM or URRM) d2x/dt2 = a = constant 10. What is projectile motion? When a particle is thrown/projected at an angle with an initial velocity, it will trace a parabola on a vertical plane and the particle is called projectile. We get the motion of the projectile, which is combination of horizontal and vertical motions. Note: Problems may asked to find acceleration, velocity, displacement etc., Equations of motion: S=ut+1/2 at2 V2-u2 = 2aS V=u+at Here, S-displacement, in m a- acceleration, in m/s2 u- initial velocity, in m/s (Initial velocity will be zero when particle starts from rest or released from rest) V-final velocity, in m/s (Final velocity will be zero when particle comes to rest) t- time, in seconds