Question

A 1400 kg wrecking ball hangs from a 20-m-long cable. the ball is pulled back until the cable makes an angle of 30.0 ∘ with the vertical.part aby how much has the gravitational potential energy of the ball changed?

Answer 1

From the geometry of the problem, the 20 m-long cable creates the hypotenuse of a right triangle, with the extended of the other two sides of size 20 m * cos(30 deg), which is around 17.3 m. Therefore, the ball has increased by 20 m - 17.3 m = 2.7 m. 

The potential energy will have altered by m*g*h, which is 1400 kg * 9.8 m/s^2 * 1.6 m , or about 37044 joules.

Answer 2

The gravitational potential energy of the ball changes by about

37000 J

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Further explanation

Let's recall the formula of Gravitational Potential Energy as follows:

$\large {\boxed {E_p = mgh }$

Ep = Gravitational Potential Energy ( Newton )

m = Object's Mass ( kg )

g = Gravitational Acceleration ( m )

h = Height ( m )

Let us now tackle the problem !

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Given:

mass of wrecking ball = m = 1400 kg

length of the cable = L = 20 m

angle with the vertical = θ = 30.0°

Asked:

gravitational potential energy = Ep = ?

Solution:

$Ep = m g h$

$Ep = m g (L - L\cos \theta)$

$Ep = 1400 ( 9.8 ) ( 20 - 20 \cos 30^o )$

$Ep = 13720 ( 20 - 10\sqrt{3} )$

$Ep \approx 37000 \texttt{ J}$

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Conclusion:

The gravitational potential energy of the ball changes by about

37000 J

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Learn more

• Impacts of Gravity : https://brainly.com/question/5330244
• Effect of Earth’s Gravity on Objects : https://brainly.com/question/8844454
• The Acceleration Due To Gravity : https://brainly.com/question/4189441
• Newton's Law of Motion: https://brainly.com/question/10431582
• Example of Newton's Law: https://brainly.com/question/498822

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Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics