The bob of a pendulum is released from a horizontal position. If the length of the pendulum is 1.5 m, what is the speed with which the bob arrives at the lowermost point, given that it dissipated 5% of its initial energy against air resistance?

Asked by Pragya Singh | 1 year ago |  151

##### Solution :-

Length of the pendulum, l= 1.5 m

Potential of the bob at the horizontal position = mgh = mgl

The initial energy dissipated against air resistance when the bob moves from the horizontal position to the lowermost point= 5%

The total kinetic energy of the bob at the lowermost position = 95% of the total potential energy at the horizontal position

($$\dfrac{1}{2}$$)mv2 = ($$\dfrac{95}{100}$$) mgl

v2 =2 [($$\dfrac{95}{100}$$) x 9.8 x 1.5]

v2 =2 ( 13.965) = 27.93

v = $$\sqrt{27.93}$$ = 5.28 m/s

Answered by Pragya Singh | 1 year ago

### Related Questions

#### How much work does she do against the gravitational force?

A person trying to lose weight (dieter) lifts a 10 kg mass, one thousand times, to a height of 0.5 m each time. Assume that the potential energy lost each time she lowers the mass is dissipated.

(a) How much work does she do against the gravitational force?

(b) Fat supplies 3.8 × 107J of energy per kilogram which is converted to mechanical energy with a 20% efficiency rate. How much fat will the dieter use up?

#### The windmill sweeps a circle of area A with their blades. If the velocity of the wind is perpendicular to the circle

The windmill sweeps a circle of area A with their blades. If the velocity of the wind is perpendicular to the circle, find the air passing through it in time t and also the kinetic energy of the air. 25 % of the wind energy is converted into electrical energy and v = 36 km/h, A = 30 m2 and the density of the air is 1.2 kg m-3. What is the electrical power produced?

#### A body of mass 0.5 kg travels in a straight line with velocity v =ax 3/2 where a = 5 m–1/2 s–1.

A body of mass 0.5 kg travels in a straight line with velocity $$v =ax^\dfrac{3}{2}$$ where$$a = 5 m^\dfrac{-1}{2}s^{–1}$$ What is the work done by the net force during its displacement from x = 0 to x = 2 m?

A ball A which is at an angle $$30^{\circ}$$ to the vertical is released and it hits a ball B of same mass which is at rest. Does the ball A rises after collision? The collision is an elastic collision.