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Chapter 6: Problem 11

a) If you jump off a table onto the floor, is your mechanical energy conserved? If not, where does it go? b) A car moving down the road smashes into a tree. Is the mechanical energy of the car conserved? If not, where does it go?

Short Answer

Expert verified
a) A person jumping off a table onto the floor. b) A car moving down the road and smashing into a tree. Answer: a) Mechanical energy is not conserved in this scenario. As the person falls, energy is lost to air resistance, sound energy upon impact, and internal energy transferred to the tissues of the body. b) Mechanical energy is also not conserved in this case. The car's kinetic energy is transformed into other forms of energy such as internal energy of the car's deformation, heat, and energy transferred to the tree and the ground (in the form of vibrations and sounds).

Step by step solution

01

Understand the conservation of mechanical energy

The principle of conservation of mechanical energy states that the total mechanical energy of an isolated system remains constant if no non-conservative forces, such as friction or air resistance, are acting on the system.
02

Analyze the situation of the jump

Initially, when the person is on the table, they have gravitational potential energy. As they jump and fall to the floor, this potential energy is converted into kinetic energy.
03

Determine if mechanical energy is conserved

As the person falls, air resistance acts as a non-conservative force. When they reach the ground, energy will be lost to the surroundings in the form of sound energy (the sound produced upon impact) and internal energy (energy transferred to the tissues of the body upon impact). Thus, the mechanical energy is not conserved in this scenario. For scenario (b):
04

Understand the conservation of mechanical energy

As mentioned earlier, the principle of conservation of mechanical energy states that the total mechanical energy of an isolated system remains constant if no non-conservative forces are acting on the system.
05

Analyze the car's motion and impact

Before the collision, the car has kinetic energy due to its motion. Upon smashing into the tree, the car comes to a stop.
06

Determine if mechanical energy is conserved

The mechanical energy of the car is not conserved in this case, as non-conservative forces act on it during the collision. These forces include friction between the car and the road, the force exerted by the tree on the car, and internal forces within the car itself. The kinetic energy of the car is transformed into other forms of energy, such as the internal energy of the car's deformation and heat, and energy transferred to the tree and the ground (vibrations and sounds).

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Most popular questions from this chapter

Can the potential energy of a spring be negative?

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