A child whose weight is 287 N slides down a 6.60 m playground slide that makes an angle of 34.0° with the horizontal. The coefficient of kinetic friction between slide and child is 0.190. (a) How much energy is transferred to thermal energy? (b) If she starts at the top with a speed of 0.516 m/s, what is her speed at the bottom? (a) Number (b) Number i Units Units 4
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.
![### Physics Problem - Friction on an Inclined Slide
**Problem Statement:**
A child whose weight is 287 N slides down a 6.60 m playground slide that makes an angle of 34.0° with the horizontal. The coefficient of kinetic friction between the slide and the child is 0.190.
**Questions:**
(a) How much energy is transferred to thermal energy?
**Answer (a):**
- Number: [Input Field]
- Units: [Input Field]
(b) If she starts at the top with a speed of 0.516 m/s, what is her speed at the bottom?
**Answer (b):**
- Number: [Input Field]
- Units: [Input Field]
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### Explanation:
1. **Understanding the Problem:**
- The child slides down a slide inclined at 34.0° to the horizontal.
- Her weight is 287 N, which implies her mass can be calculated using the gravitational acceleration (Weight = Mass × g).
- The friction along the slide is characterized by a coefficient of kinetic friction, μ_k = 0.190.
2. **Thermal Energy Calculation:**
- When the child slides down, work is done against friction.
- The work done by friction (which is converted to thermal energy) can be calculated.
3. **Final Speed Calculation:**
- Using the conservation of energy principle or kinematic equations, consider the initial kinetic energy, potential energy, and the work done against friction to find the final speed at the bottom.
Graphical representations might include:
- A diagram of the slide showing the angle of inclination.
- Free body diagrams displaying forces acting on the child (e.g., gravitational force, normal force, frictional force).
**Reminder:** Ensure to use the correct units for all calculations and inputs.
**Note:** Any error messages or invalid inputs might be indicated visually, along with feedback for incorrect attempts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4498e0d-5915-421f-a7a7-3ad8a56e2358%2Fcac5b4a4-4c2c-4552-8bcd-b63615c84f73%2Ftn6tylk_processed.jpeg&w=3840&q=75)
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