Answer:
a). Gravitational Potential energy= 294 Joules
b). when the ropes make a 25.0°
Gravitational Potential energy= 27.55 Joules
C).Gravitational Potential energy= 0 Joules
Explanation:
GPE (gravitational potential energy ) is always relative to some zero reference point. For swings, it makes sense to set GPE = 0 at the bottom of the swing's arc where theta = 0 deg relative to the vertical.
In general GPE (gravitational potential energy ) = mgh;
where mg = 140 N is the weight of the child with mass m,
g is the gravity field, and
h is the height above the zero reference.
In general, from ordinary trig, we have h = L(1 - cos(theta))
where L = 2.1 m is the length of each rope.
Gravitational Potential energy = mgh
Gravitational Potential energy
= 140 × L(1 - cos(90))
= 140 × 2.10(1 - 0)
= 294joules
b) GPE = 140*2.1(1 - cos(25))
Gravitational Potential energy
= 140 × L(1 - cos(25))
= 140 × 2.10(1 - 0.9063)
= 140 × 2.10(0.0937)
= 140 × 0.19677
=27.55 joules
c)
GPE = 0 or
= 140*2.1(1 - cos(0))
= 0
a. The gravitational potential energy (in Joules) of the child-earth system when the ropes are horizontal is 294 Joules.
b. The gravitational potential energy (in Joules) of the child-earth system when the ropes make a 25.0° angle with the vertical is 28 Joules.
c. The gravitational potential energy (in Joules) of the child-earth system when the child is at the bottom of the circular arc is 0 Joules.
Given the following data:
To find the gravitational potential energy (in Joules) of the child-earth system relative to the child's lowest position at the following times:
Mathematically, gravitational potential energy (G.P.E) is given by the formula;
[tex]G.P.E = mgh[/tex]
Where:
a. When the ropes are horizontal:
First of all, we would find the height of the child.
For a swing, the height is given by the formula:
[tex]h = L(1 - cos \theta)[/tex]
At an horizontal, the angle = 90°
[tex]h = L(1 - cos \theta)\\\\h = 2.1(1 - cos90)\\\\h = 2.1(1 - 0)\\\\h=2.1\times 1[/tex]
h = 2.1 meters
[tex]G.P.E = 140 \times 2.1[/tex]
G.P.E = 294 Joules.
b. When the ropes make a 25.0° angle with the vertical:
[tex]h = L(1 - cos \theta)\\\\h = 2.1(1 - cos25)\\\\h = 2.1(1 - 0.9063)\\\\h=2.1\times 0.0937[/tex]
h = 0.20 meters
[tex]G.P.E = 140 \times 0.20[/tex]
G.P.E = 28 Joules.
c. When the child is at the bottom of the circular arc:
The angle at the bottom of the circular arc formed by the swing is zero (0) degrees.
[tex]h = L(1 - cos \theta)\\\\h = 2.1(1 - cos0)\\\\h = 2.1(1 - 1)\\\\h=2.1\times 0[/tex]
h = 0 meters
[tex]G.P.E = 140 \times 0[/tex]
G.P.E = 0 Joules.
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