Kinetics of a particle: Work & Energy

Objectives To develop the principle of work and energy and apply it to solve problems that involve force, velocity, and displacement. To study problems that involve power and efficiency. To introduce the concept of a conservative force and apply the theorem of conservation of energy to solve kinetic problems. 14/11/61 MEE214 – Dynamics

Work of a Force A force F does work on a particle only when the particle undergoes a displacement in the direction of the force. 14/11/61 MEE214 – Dynamics

Work of a Force If the particle undergoes a finite displacement along its path from r1 to r2 or s1 to s2, the work is determined by integration. 14/11/61 MEE214 – Dynamics

Work of a Weight 14/11/61 MEE214 – Dynamics

Work of a Spring Force Work done on a spring Force and Displacement are in the same direction. 14/11/61 MEE214 – Dynamics

Work of a Spring Force Work done on a particle or body Force and Displacement are in the different direction. 14/11/61 MEE214 – Dynamics

Example 14.1 The 10-kg block rest on a smooth incline. If the spring is originally stretched 0.5 m, determine the total work done by all forces acting on the block when a horizontal force P = 400 N pushes the block up the plane s = 2 m. 14/11/61 MEE214 – Dynamics

Principle of Work and Energy Consider a particle P, which at the instant considered located on the path as measured from an inertial coordinate system. For the particle in the tangential direction, ∑Ft = mat 14/11/61 MEE214 – Dynamics

Principle of Work and Energy 14/11/61 MEE214 – Dynamics

Problem 14-13 The 2-lb brick slides down a smooth roof, such that when it is at A it has a velocity of 5 ft/s Determine the speed of the brick just before it leaves the surface at B, the distance d from the wall to where it strikes the ground, and the speed at which it hits the ground. 14/11/61 ME212 ดร. พิภัทร

Example 14.6 The block A and B have a mass of 10-kg and 100-kg respectively. Determine the distance B travels from the point where it is released from rest to the point its speed become 2 m/s. 14/11/61 MEE214 – Dynamics

Example 14.4 The platform P is tied down so that the 0.4-m-long cords keep a 1-m-long spring compressed 0.6-m when nothing is on the platform. If a 2-kg platform is placed on the platform and released from rest after the platform is pushed down 0.1 m, determine the max height h the block rises in the air, measure from the ground. 14/11/61 MEE214 – Dynamics

Power v Power It is defined as the amount of work performed per unit of time. The power generated by a machine or engine that performs an amount of work dU within a time interval dt is 14/11/61 MEE214 – Dynamics

Efficiency Efficiency It is defined as the ratio of the output of useful power produced by the machine to the input of power supplied to the machine 14/11/61 MEE214 – Dynamics

Example 14.8 The motor M of the hoist operates with an efficiency of ε = 0.85. Determine the power that must be supplied to the motor to lift the 375-N crate C at the instant point P on the cable has an acceleration of 1.2m/s2, and a velocity of 0.6 m/s 14/11/61 MEE214 – Dynamics

Conservative Force Work done is independent of the path Examples: Weight of a particle Elastic force of a spring 14/11/61 MEE214 – Dynamics

Potential Energy Amount of work done by a conservative force from moving from a given position to datum. Capacity of work stored in a particle. 14/11/61 MEE214 – Dynamics

Potential Energy 14/11/61 MEE214 – Dynamics

Conservation of Energy If a particle is subject to both conservative and non-conservative forces: No non-conservative forces: 14/11/61 MEE214 – Dynamics