A rubber ballI, with a mass of 40.0 grams is dropped from rest from a height of 1.20 m above the floor. It hits the floor, and then reaches a maximum height of 80.0 cm when it comes back up again. In this problem, use g = 10.0 m/s?. (a) The collision with the floor causes some mechanical energy to be lost (this energy generally ends up as thermal energy). How much mechanical energy is lost in this case? (b) What is the ball's speed, just as it leaves the floor on its way up? m/s (c) What is the magnitude of the impulse experienced by the ball for the entire time it is in contact with the floor? kg • m/s
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.
![**Problem Description:**
A rubber ball, with a mass of 40.0 grams, is dropped from rest from a height of 1.20 m above the floor. It hits the floor and then reaches a maximum height of 80.0 cm when it comes back up again. In this problem, use \( g = 10.0 \, \text{m/s}^2 \).
**Questions:**
(a) The collision with the floor causes some mechanical energy to be lost (this energy generally ends up as thermal energy). How much mechanical energy is lost in this case?
- [ ] J
(b) What is the ball's speed, just as it leaves the floor on its way up?
- [ ] m/s
(c) What is the magnitude of the impulse experienced by the ball for the entire time it is in contact with the floor?
- [ ] kg \(\cdot\) m/s
**Guide for Solution:**
1. **Convert Units:**
- Mass: \( 40.0 \, \text{grams} = 0.040 \, \text{kg} \).
- Convert the maximum height from cm to meters: \( 80.0 \, \text{cm} = 0.80 \, \text{m} \).
2. **Calculate Initial Potential Energy:**
- \( PE_{\text{initial}} = mgh = 0.040 \times 10.0 \times 1.20 \).
3. **Calculate Final Potential Energy:**
- \( PE_{\text{final}} = mgh = 0.040 \times 10.0 \times 0.80 \).
4. **Determine Energy Loss:**
- \( \text{Energy Lost} = PE_{\text{initial}} - PE_{\text{final}} \).
5. **Find Speed as it Leaves the Floor:**
- Using energy conservation principles on the way up to find speed.
6. **Calculate Impulse:**
- Impulse involves change in momentum and can be calculated by considering before and after collision velocities.
Follow these steps to find the answers to each question, applying necessary physics formulas for potential energy, kinetic energy, and momentum.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5ea9d1b2-8f99-46bf-8a92-8bbfd1b1e697%2Fbd5a2c93-cbed-4f8f-9dc1-faedc000ea72%2F5xh29dp_processed.png&w=3840&q=75)
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