Two railroad cars, each of mass 5819kg and traveling 108km/h in opposite directions, collide head-on and come to rest. How much thermal energy is produced in this collision?
Kinematics
A machine is a device that accepts energy in some available form and utilizes it to do a type of work. Energy, work, or power has to be transferred from one mechanical part to another to run a machine. While the transfer of energy between two machine parts, those two parts experience a relative motion with each other. Studying such relative motions is termed kinematics.
Kinetic Energy and Work-Energy Theorem
In physics, work is the product of the net force in direction of the displacement and the magnitude of this displacement or it can also be defined as the energy transfer of an object when it is moved for a distance due to the forces acting on it in the direction of displacement and perpendicular to the displacement which is called the normal force. Energy is the capacity of any object doing work. The SI unit of work is joule and energy is Joule. This principle follows the second law of Newton's law of motion where the net force causes the acceleration of an object. The force of gravity which is downward force and the normal force acting on an object which is perpendicular to the object are equal in magnitude but opposite to the direction, so while determining the net force, these two components cancel out. The net force is the horizontal component of the force and in our explanation, we consider everything as frictionless surface since friction should also be calculated while called the work-energy component of the object. The two most basics of energy classification are potential energy and kinetic energy. There are various kinds of kinetic energy like chemical, mechanical, thermal, nuclear, electrical, radiant energy, and so on. The work is done when there is a change in energy and it mainly depends on the application of force and movement of the object. Let us say how much work is needed to lift a 5kg ball 5m high. Work is mathematically represented as Force ×Displacement. So it will be 5kg times the gravitational constant on earth and the distance moved by the object. Wnet=Fnet times Displacement.
![Two railroad cars, each of mass 5819 kg and traveling 108 km/h in opposite directions, collide head-on and come to rest. How much thermal energy is produced in this collision?
*Explanation:*
In this problem, two railroad cars of equal mass are traveling at the same speed but in opposite directions. When they collide head-on and come to rest, the kinetic energy of each car is converted into thermal energy. To find the thermal energy produced, we need to calculate the initial kinetic energy of the system and use the principle of conservation of energy.
*Detailed Steps:*
1. **Convert the speed from km/h to m/s:**
\[ 108 \, \text{km/h} = \frac{108 \times 1000 \, \text{m}}{3600 \, \text{s}} = 30 \, \text{m/s} \]
2. **Calculate the kinetic energy of each car:**
\[ KE = \frac{1}{2}mv^2 \]
Substituting the values,
\[ KE = \frac{1}{2} \times 5819 \, \text{kg} \times (30 \, \text{m/s})^2 \]
\[ KE = \frac{1}{2} \times 5819 \times 900 \]
\[ KE = 2618550 \, \text{J (Joules)} \]
3. **Calculate the total kinetic energy of the two cars:**
Since there are two cars,
\[ Total \, KE = 2 \times 2618550 \, \text{J} = 5237100 \, \text{J} \]
4. **Determine the thermal energy produced:**
As the cars come to rest, all initial kinetic energy is converted to thermal energy.
\[ Thermal \, Energy = 5237100 \, \text{J} \]
Thus, 5237100 Joules of thermal energy is produced in the collision.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4211b25e-5640-4e59-912c-e01e8955356b%2F787006fc-81e0-4abe-adc1-a9cd8fbd461c%2Flgwgeoe_processed.jpeg&w=3840&q=75)
Step by step
Solved in 3 steps
