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A 125 kg wrecking ball on a 15.4 m

long cable is pulled back to an
angle of 33.5° and released. How
much KE does it have at the
bottom of its swing?
(Unit = J)

2 Answers

5 votes

Final answer:

To find the kinetic energy at the bottom of the wrecking ball's swing, calculate the initial height using trigonometry, then use it to determine the potential energy, which is equal to the kinetic energy at the bottom due to energy conservation.

Step-by-step explanation:

Calculating Kinetic Energy of a Wrecking Ball

To calculate the kinetic energy (KE) at the bottom of its swing for a 125 kg wrecking ball on a 15.4 m cable released from a 33.5° angle, we use the principle of conservation of energy. Initially, the wrecking ball has potential energy (PE) due to its height, which is converted to kinetic energy at the bottom of the swing. The height (h) can be found using trigonometry, h = L - Lcos(θ), where L is the length of the cable and θ is the angle with the vertical. Then, calculate the initial potential energy using PE = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s²), and h is the height calculated. As there are no energy losses mentioned (such as air resistance), the kinetic energy at the bottom of the swing will equal the initial potential energy.

To find the height: h = 15.4 m - 15.4m × cos(33.5°).

Once h is found, calculate:

PE_initial = m × g × h

Finally, KE_bottom = PE_initial, as energy is conserved.

User Kalamar Obliwy
by
7.8k points
5 votes

here is the answer hope it will help

A 125 kg wrecking ball on a 15.4 m long cable is pulled back to an angle of 33.5° and-example-1
User Notihs
by
9.2k points