1.The powr developed by a force is --- and that of couple is ---
2. The velocity of cylinder which is released from rest on 0 degree incline after it has rolled through a distance l is given by ---
3.The conditions for none slipping are ------
4. The direction of cariloes acceleration is obtained by ----
5 The action of a spring on a movable body to which it is attached is a common example of ---
1. The power developed by a force is given by the product of the force and the velocity at which the force is applied. Mathematically, it can be represented as:
Power = Force × Velocity
On the other hand, the power of a couple is given by the product of one of the forces in the couple and the angular velocity. Mathematically, it can be represented as:
Power = Force (in the couple) × Angular Velocity
2. The velocity of a cylinder that is released from rest on a 0-degree incline after it has rolled through a distance "l" can be determined using the principle of conservation of energy. The gravitational potential energy at the starting point is converted into the kinetic energy at the bottom of the incline.
Using the conservation of energy, the velocity "v" can be calculated using the equation:
mgh = (1/2)mv^2
where m is the mass of the cylinder, g is the acceleration due to gravity, h is the height from the starting point to the bottom of the incline, and v is the velocity.
3. The conditions for non-slipping in a rotating system can be stated as follows:
- The object must have sufficient friction with the surface or medium it is in contact with.
- The tangential speed of the rotating object must be such that the frictional force can provide the necessary centripetal force.
- The radius of the object's path must be such that the frictional force can provide the necessary centripetal force.
If these conditions are met, the object will rotate without slipping.
4. The direction of centripetal acceleration, which is the acceleration pointing towards the center of the circular path, can be determined using the following steps:
- Identify the velocity vector of the object at a particular point on the circular path.
- Draw a vector from that point to the center of the circular path.
- The direction of this vector points towards the center of the circular path. This is the direction of the centripetal acceleration.
5. The action of a spring on a movable body to which it is attached is a common example of simple harmonic motion (SHM). In SHM, the body oscillates back and forth around an equilibrium position under the influence of a restoring force.
The restoring force provided by the spring is directly proportional to the displacement of the body from the equilibrium position, and it acts in the opposite direction to the displacement. This relationship is described by Hooke's Law:
F = -kx
Where F is the force, k is the spring constant, and x is the displacement from the equilibrium position.
Therefore, the spring force acts as a restoring force, bringing the body back towards the equilibrium position when displaced. This leads to the oscillatory motion observed in systems involving springs.