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Chapter 6: Problem 20

Sean climbs a tower that is \(82.3 \mathrm{m}\) high to make a jump with a parachute. The mass of Sean plus the parachute is \(68.0 \mathrm{kg} .\) If \(U=0\) at ground level, what is the potential energy of Sean and the parachute at the top of the tower?

Short Answer

Expert verified
Answer: The gravitational potential energy of Sean and the parachute at the top of the tower is approximately 55431.164 Joules (J).

Step by step solution

01

Write the formula for potential energy

To find the potential energy of Sean and the parachute at the top of the tower, we will use the formula for gravitational potential energy: \(PE = mgh\).
02

Identify the values given by the exercise

The height of the tower, \(h\), is 82.3 meters (m), and the mass of Sean plus the parachute, \(m\), is 68.0 kilograms (kg). The gravitational acceleration, \(g\), is approximately 9.81 meters per second squared (\(m/s^2\)).
03

Substitute the given values into the formula and solve

We can now substitute the given values into the potential energy formula: \(PE = mgh = (68.0\,\mathrm{kg})(9.81\,\mathrm{m/s^2})(82.3\,\mathrm{m})\) Now, we can calculate the potential energy: \(PE = (68.0)(9.81)(82.3) = 55431.164\,\mathrm{J}\) So, the potential energy of Sean and the parachute at the top of the tower is approximately 55431.164 Joules (J).

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Most popular questions from this chapter

Rachel is on the roof of a building, \(h\) meters above ground. She throws a heavy ball into the air with a speed \(v,\) at an angle \(\theta\) with respect to the horizontal. Ignore air resistance. (a) Find the speed of the ball when it hits the ground in terms of \(h, v, \theta,\) and \(g .\) (b) For what value(s) of \(\theta\) is the speed of the ball greatest when it hits the ground?
In Section \(6.2,\) Rosie lifts a trunk weighing \(220 \mathrm{N}\) up $4.0 \mathrm{m} .\( If it take her \)40 \mathrm{s}$ to lift the trunk, at what average rate does she do work?
Sam pushes a \(10.0-\mathrm{kg}\) sack of bread flour on a frictionless horizontal surface with a constant horizontal force of \(2.0 \mathrm{N}\) starting from rest. (a) What is the kinetic energy of the sack after Sam has pushed it a distance of \(35 \mathrm{cm} ?\) (b) What is the speed of the sack after Sam has pushed it a distance of \(35 \mathrm{cm} ?\)
The bungee jumper of Example 6.4 made a jump into the Gorge du Verdon in southern France from a platform \(182 \mathrm{m}\) above the bottom of the gorge. The jumper weighed \(780 \mathrm{N}\) and came within \(68 \mathrm{m}\) of the bottom of the gorge. The cord's unstretched length is \(30.0 \mathrm{m}\) (a) Assuming that the bungee cord follows Hooke's law when it stretches, find its spring constant. [Hint: The cord does not begin to stretch until the jumper has fallen \(30.0 \mathrm{m} .]\) (b) At what speed is the jumper falling when he reaches a height of \(92 \mathrm{m}\) above the bottom of the gorge?
A plane weighing \(220 \mathrm{kN} \quad(25 \text { tons })\) lands on an aircraft carrier. The plane is moving horizontally at $67 \mathrm{m} / \mathrm{s}(150 \mathrm{mi} / \mathrm{h})$ when its tailhook grabs hold of the arresting cables. The cables bring the plane to a stop in a distance of $84 \mathrm{m}$ (a) How much work is done on the plane by the arresting cables? (b) What is the force (assumed constant) exerted on the plane by the cables? (Both answers will be underestimates, since the plane lands with the engines full throttle forward; in case the tailhook fails to grab hold of the cables, the pilot must be ready for immediate takeoff.)
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