POWER A-LEVEL PHYSICS

POWER

It is the rate of doing work.

Example

1. A particle of mass 1000kg moves with uniform velocity of 10ms^-1 up a straight truck inclined at an angle of 20° to the horizontal. The total frictional resistance to motion of the car is 248N. Calculate the power developed in the engine.

2. Sand is deposited at a uniform rate of 20kgs^-1 and of negligible kinetic energy onto an empty conveyor belt moving horizontally at a constant speed of 10m / minute.

Find

• A force required to maintain a constant velocity.
• The power required to maintain a constant velocity
• The rate of change of K.E of the moving sand
• Why are the latter 2 quantities unequal?

The two quantities are not equal because there is a frictional force that has to be overcome.

THIS VIDEO IS ABOUT POWER IN ADVANCED PHYSICS

MOMENTS AND COUPLES

Moment of a force

The moment of a force about an axis is the product of the force and the perpendicular distance from the axis to the line of action of the force.

Moment of F₁ about P

= F₁a

Moment of R about P = 0

Moment of T about P = T. a sin Ө

Principal of moments

If a body is in equilibrium, under the action of a number of force, the algebraic sum of the moment of the forces about any axis is zero i.e. total clockwise moments = total anticlockwise moments about the same axis.

Conditions for equilibrium

• Translational equilibrium.

The resultant force must be zero i.e. sum of forces in one direction should be equal to sum of forces in the opposite direction.

• Rotational equilibrium

The algebraic sum of moments about any axis must be zero.

Example

A uniform rod of mass 10kg is smoothly hinged at A and rests in a vertical plane on the end B against a smooth vertical wall. If the rod makes an angle of  40⁰ with the wall, find the thrust of the wall and the direction of the reaction at A

Let X and Y represent the components of the reaction in the horizontal and vertical directions respectively.

Resolving forces in the horizontal direction

R = X

Resolving forces in the vertical direction

Y  = 10g = 98N

Taking moments about A:

10gx(ABsin40)/2 = R xABcos40

Therefore R = 41.1N

Hence X = 41.1N

THIS VIDEO EXPLAINS MORE ABOUT COUPLES AND MOMENTS

CIRCULAR MOTION

Suppose the body moves from point A to point B in time‘t’ through an angle Ө.

The angle Ө is called the angular displacement.

Arc length, s = r Ө

Angular velocity, w, is the rate of change of angular displacement.

 Acceleration of a body moving in a circle

Consider a body moving with constant speed v in a circle of radium r

If it travels from A to B in a short time,¶t,

The acceleration of the body moving in a circle is towards the centre of the circle.

The force on a body moving in a circle towards the centre of the circular path is called the centripetal force

Example of circular motion

Conical pendulum

Example

A steel ball of 0.5kg is suspended from a light inelastic string of length 1m. The ball describes a horizontal circle of radius 0.5m

Find

• The centripetal speed of the ball
• The angular speed of the ball
• The angle between the string and the radius of the circle if the angular speed is increased to such a values that the tension in the string is 10N

Vehicle on a curved track

• Overturning / upsetting / toppling

consider a vehicle with mass m moving with a speed v in a circle of radius r; let h be the height of the centre of gravity above the truck and 2a the distance between the tyres.

The vehicle is likely to overturn if

• The bend is sharp (r is small)
• The centre of gravity is high (h is large)
• The distance between the tires is small (a is small)

Skidding

A vehicle will skid when the available centripetal force is not enough to balance the centrifugal force (force away from the centre of the circle), the vehicle fails to negotiate the curve and goes off truck outwards.

For no skidding, the centripetal force must be greater or equal to the centrifugal force i.e.

Skidding will occur if

• The vehicle is moving too fast
• The bend is too sharp (r is small)
• The road is slippery (μ is small )

THIS VIDEO IS ABOUT CIRCULAR MOTION IN PHYSICS

BANKING OF A TRACK

• This is the building of the track round a corner with the outer edge raised above the inner one. This is done in order to increase the maximum safe speed for no skidding.
• When a road is banked, some extra centripetal force is provided by the horizontal component of the normal reaction
• When determining the angle of banking during the construction of the road, friction is ignored.

When there is friction

Suppose  there is friction between the track and the vehicle moving round the bend.

Motion in a vertical circle

This is an example of motion in a circle with non- uniform speed. The body will have a radial component of acceleration as well as a tangential component. Consider a particle of mass is attached to an inextensible string at point O, and projected from the lowest point P with a speed U so that it describes a vertical circle.

Consider a particle at point Q at subsequent time.

The tension T in the string is everywhere normal to the path of the particle and hence to its velocity V. the tension therefore does no work on the particle.

Energy at P, E_P is E_p = ½mu² ……………………..(1)

P is the reference for zero potential . Energy at Q in E_q is:-

E_q =  ½mv² + mgh.

But h = r-rcosӨ

Eq =  ½ mv² + mgr (1-cosӨ) ………………….(2)

Example

1. A cyclist rounds a curve of 30m radius on a road which is banked at an angle of 20⁰ to the horizontal. If the co-efficient of sliding friction between the tires and the road is 0.5; find the greatest speed at which the cyclist can ride without skidding and find into inclination to the horizontal at this speed.