All the boxes shown below were initially at rest. Then they were pushed 5 m (meters) across the floor by a net horizontal force. Rank the change in kinetic energy of the boxes for the interval they were being pushed.
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.
Please help!
![**Educational Website Content: Kinetic Energy and Force Application**
In this exercise, we are analyzing the change in kinetic energy of various boxes when pushed by different net forces over a distance. All the boxes were initially at rest and then pushed 5 meters (m) across the floor by a net horizontal force. Your task is to rank the change in kinetic energy of these boxes during the interval they were being pushed.
### Box Configurations:
1. **Box P:**
- Net Force (\( F_{\text{net}} \)): 75 N
- Mass: 25 kg
2. **Box Q:**
- Net Force (\( F_{\text{net}} \)): 75 N
- Mass: 50 kg
3. **Box R:**
- Net Force (\( F_{\text{net}} \)): 50 N
- Mass: 75 kg
4. **Box S:**
- Net Force (\( F_{\text{net}} \)): 50 N
- Mass: 25 kg
5. **Box T:**
- Net Force (\( F_{\text{net}} \)): 25 N
- Mass: 50 kg
6. **Box U:**
- Net Force (\( F_{\text{net}} \)): 25 N
- Mass: 75 kg
### Task:
Rank the boxes based on the change in kinetic energy as they are being pushed over the distance of 5 meters. Use the work-energy principle, where the work done by the force is equal to the change in kinetic energy.
### Options for Ranking:
1. \( Q = R > P = U > S = T \)
2. \( P = Q > R = S > T = U \)
3. \( Q > P = R > S > U > T \)
4. \( R = U > Q = T = P = S \)
Select the correct option based on your analysis of the force and mass of each box, understanding of how work translates to changes in kinetic energy.
### Hint:
Use the equation for work done:
\[ \text{Work} = F_{\text{net}} \times d \]
Where \( d = 5 \, \text{m} \). Since all boxes are pushed the same distance, compare the products of force and mass inversely to understand how they affect changes in kinetic](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa9566eaa-b3a3-4ccc-8f7e-dc0e3b526c2b%2F3845941f-1d3e-4141-bdc2-74e63e920903%2Fm0j479_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
