Physics, 26.06.2019 00:10 djtblaster

Apendulum of length l=36.1 cm and mass m=168 g is released from rest when the cord makes an angle of 65.4 degrees with the vertical. (a) how far does the mass fall (y-displacement) before reaching its lowest point? (b) how much work is done by gravity as it falls to its lowest point? (c) how much work is done by the string tension as it falls to its lowest point?

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Answer from: kidus24

A pendulum of length L=36.1 cm and mass m=168 g is released from rest gives the values as,

a) The distance where the mass fall (y-displacement) before reaching its lowest point is 21.1 meter away.(b) Work is done by gravity as it falls to its lowest point is 0.347 joules(c) Work is done by the string tension as it falls to its lowest point is 0.What is work done of pendulum?

Work done of a pendulum is always against the gravitational force. The pendulum losses the kinetic energy and gains the potential energy.

Given information-

The length of the pendulum is 36.1 cm.

The mass of the pendulum is 168 grams.

The angle made by the cord is 65.4 degrees.

(a) The distance where the mass fall (y-displacement) before reaching its lowest point-

The distance where the mass fall (y-displacement) before reaching its lowest point is the difference of the length of the pendulum along the horizontal direction and the length of the pendulum. Thus,

$d=36.1\cos(65.4)-36.1\\d=-21.1\rm cm$

Thus the distance where the mass fall (y-displacement) before reaching its lowest point is 21.1 meter away.

(b) Work is done by gravity as it falls to its lowest point-

Work done by gravity to fall the mass at 21.1 meter away is,

$W=0.168\times9.8\times0.211\\W=0.347\rm J$

Thus the work is done by gravity as it falls to its lowest point is 0.347 joules.

Work is done by the string tension as it falls to its lowest point is,

$W=0.168\times0.211\times\cos(90)\\W=0$

Thus, the work is done by the string tension as it falls to its lowest point is 0.

Learn more about the work done of pendulum here;

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Answer from: NeverEndingCycle

(a) -0.211 m

At the beginning the mass is displaced such that the length of the pendulum is L = 36.1 cm and the angle with the vertical is

$\theta=65.4^{\circ}$

The projection of the length of the pendulum along the vertical direction is

$L_y = L cos \theta = (36.1 cm)(cos 65.4^{\circ})=15.0 cm$

the full length of the pendulum when the mass is at the lowest position is

L = 36.1 cm

So the y-displacement of the mass is

$\Delta y = 15.0 cm - 36.1 cm = -21.1 cm = -0.211 m$

(b) 0.347 J

The work done by gravity is equal to the decrease in gravitational potential energy of the mass, which is equal to

$\Delta U = mg \Delta y$

where we have

m = 168 g = 0.168 kg is the mass of the pendulum

g = 9.8 m/s^2 is the acceleration due to gravity

$\Delta y = 0.211 m$ is the vertical displacement of the pendulum

So, the work done by gravity is

W=(0.168 kg)(9.8 m/s^2)(0.211 m)=0.347 J

And the sign is positive, since the force of gravity (downward) is in the same direction as the vertical displacement of the mass.

The work done by a force is:

$W=Fd cos \theta$

where

F is the magnitude of the force

d is the displacement

$\theta$ is the angle between the direction of the force and the displacement

In this situation, the tension in the string always points in a radial direction (towards the pivot of the pendulum), while the displacement of the mass is tangential (it follows a circular trajectory): this means that the tension and the displacement are always perpendicular to each other, so in the formula

$\theta=90^{\circ}, cos \theta = 0$

and so the work done is zero.

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