Engineering mechanics notes for engineering
- 1. Lecture V
- 2. Principle of Conservation of Energy -It states “The energy can neither be created nor destroyed, though it can be transformed from one form into any of the forms, in which the energy can exist.” -The loss of energy in any one form is always accompanied by an equivalent increase in another form. When work is done on a rigid body, the work is converted into kinetic or potential energy or is used in overcoming friction.
- 3. Impulse and Impulsive Force
- 4. -If a force acts for a very short time, it is then known as impulsive force or blow. The impulsive force occurs in collisions, in explosions, in the striking of a nail or a pile by a hammer. -When the two rotating gears with angular velocities ω1 and ω2 mesh each other, then an impulsive torque acts on the two gears, until they are both rotating at speeds corresponding to their velocity ratio. -The impulsive torque,
- 5. Principle of Conservation of Momentum - It states “The total momentum of a system of masses (i.e. moving bodies) in any one direction remains constant, unless acted upon by an external force in that direction.” - This principle is applied to problems on impact, i.e. collision of two bodies. In other words, if two bodies of masses m1 and m2 with linear velocities v1 and v2 are moving in the same straight line, and they collide and begin to move together with a common velocity v, then
- 6. Notes: 1. The positive sign is used when the two bodies move in the same direction after collision. The negative sign is used when they move in the opposite direction after collision. 2. Consider two rotating bodies of mass moment of inertia I1 and I2 are initially apart from each other and are made to engage as in the case of a clutch. If they reach a common angular velocity ω, after slipping has ceased, then
- 7. Worked Examples 1. A haulage rope winds on a drum of radius 500 mm, the free end being attached to a truck. The truck has a mass of 500 kg and is initially at rest. The drum is equivalent to a mass of 1250 kg with radius of gyration 450 mm. The rim speed of the drum is 0.75 m/s before the rope tightens. By considering the change in linear momentum of the truck and in the angular momentum of the drum, find the speed of the truck when the motion becomes steady. Find also the energy lost to the system.
- 10. 2. The two buffers at one end of a truck each require a force of 0.7 MN/m of compression and engage with similar buffers on a truck which it overtakes on a straight horizontal track. The truck has a mass of 10 tonnes and its initial speed is 1.8 m/s, while the second truck has mass of 15 tonnes with initial speed 0.6 m/s, in the same direction. Find : 1. the common velocity when moving together during impact, 2. the kinetic energy lost to the system, 3. the compression of each buffer to store the kinetic energy lost, and 4. The velocity of each truck on separation if only half of the energy offered in the springs is returned.
- 15. 3. A mass of 300 kg is allowed to fall vertically through 1 metre on to the top of a pile of mass 500 kg. Assume that the falling mass and pile remain in contact after impact and that the pile is moved 150 mm at each blow. Find, allowing for the action of gravity after impact 1. The energy lost in the blow, and 2. The average resistance against the pile.