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Chapter 6: Problem 10

Can the kinetic energy of an object be negative? Can the potential energy of an object be negative?

Short Answer

Expert verified
Answer: Kinetic energy of an object can never be negative as both mass and the square of velocity are always positive. However, potential energy can be negative depending on the chosen reference point for height. If the reference point is above an object's current position, the height will be negative, resulting in negative potential energy.

Step by step solution

01

Determine if kinetic energy can be negative

The formula for kinetic energy is K = (1/2)mv^2. Since the mass of an object (m) is always positive, and the square of the velocity (v^2) is also always positive, the product (1/2)mv^2 will always be positive or equal to zero. It cannot be negative, so we can conclude that the kinetic energy of an object cannot be negative.
02

Determine if potential energy can be negative

The formula for potential energy is U = mgh. The mass of an object (m) is always positive, and the acceleration due to gravity (g) is also always positive. However, the height (h) above the reference point can be either positive or negative depending on the chosen reference point. If we choose a reference point below the object's current position, the height (h) will be positive, and the potential energy (U) will be positive. However, if we choose a reference point above the object's current position, the height (h) will be negative, and the potential energy (U) will be negative. In conclusion, it's possible for the potential energy of an object to be negative depending on the chosen reference point.

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Most popular questions from this chapter

A spring has a spring constant of \(80 \mathrm{~N} / \mathrm{m}\). How much potential energy does it store when stretched by \(1.0 \mathrm{~cm} ?\) a) \(4.0 \cdot 10^{-3}\) J b) \(0.40 \mathrm{~J}\) c) 80 d) \(800 \mathrm{~J}\) e) \(0.8 \mathrm{~J}\)

A classmate throws a \(1.0-\mathrm{kg}\) book from a height of \(1.0 \mathrm{~m}\) above the ground straight up into the air. The book reaches a maximum height of \(3.0 \mathrm{~m}\) above the ground and begins to fall back. Assume that \(1.0 \mathrm{~m}\) above the ground is the reference level for zero gravitational potential energy. Determine a) the gravitational potential energy of the book when it hits the ground. b) the velocity of the book just before hitting the ground.

A block of mass \(5.0 \mathrm{~kg}\) slides without friction at a speed of \(8.0 \mathrm{~m} / \mathrm{s}\) on a horizontal table surface until it strikes and sticks to a mass of \(4.0 \mathrm{~kg}\) attached to a horizontal spring (with spring constant of \(k=2000.0 \mathrm{~N} / \mathrm{m}\) ), which in turn is attached to a wall. How far is the spring compressed before the masses come to rest? a) \(0.40 \mathrm{~m}\) b) \(0.54 \mathrm{~m}\) c) \(0.30 \mathrm{~m}\) d) \(0.020 \mathrm{~m}\) e) \(0.67 \mathrm{~m}\)

An arrow is placed on a bow, the bowstring is pulled back, and the arrow is shot straight up into the air; the arrow then comes back down and sticks into the ground. Describe all of the changes in work and energy that occur.

A 20.0 -kg child is on a swing attached to ropes that are \(L=1.50 \mathrm{~m}\) long. Take the zero of the gravitational potential energy to be at the position of the child when the ropes are horizontal. a) Determine the child's gravitational potential energy when the child is at the lowest point of the circular trajectory. b) Determine the child's gravitational potential energy when the ropes make an angle of \(45.0^{\circ}\) relative to the vertical. c) Based on these results, which position has the higher potential energy?
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