Respuesta :
(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
[tex]\theta=65.4^{\circ}[/tex]
The projection of the length of the pendulum along the vertical direction is
[tex]L_y = L cos \theta = (36.1 cm)(cos 65.4^{\circ})=15.0 cm[/tex]
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
[tex]\Delta y = 15.0 cm - 36.1 cm = -21.1 cm = -0.211 m[/tex]
(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
[tex]\Delta U = mg \Delta y[/tex]
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
[tex]\Delta y = 0.211 m[/tex] is the vertical displacement of the pendulum
So, the work done by gravity is
[tex]W=(0.168 kg)(9.8 m/s^2)(0.211 m)=0.347 J[/tex]
And the sign is positive, since the force of gravity (downward) is in the same direction as the vertical displacement of the mass.
(c) Zero
The work done by a force is:
[tex]W=Fd cos \theta[/tex]
where
F is the magnitude of the force
d is the displacement
[tex]\theta[/tex] 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
[tex]\theta=90^{\circ}, cos \theta = 0[/tex]
and so the work done is zero.
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,
[tex]d=36.1\cos(65.4)-36.1\\d=-21.1\rm cm[/tex]
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,
[tex]W=0.168\times9.8\times0.211\\W=0.347\rm J[/tex]
Thus the 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-
Work is done by the string tension as it falls to its lowest point is,
[tex]W=0.168\times0.211\times\cos(90)\\W=0[/tex]
Thus, the work is done by the string tension as it falls to its lowest point is 0.
- 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.
Learn more about the work done of pendulum here;
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