Chapter 6: Problem 25
A sled with mass 12.00 kg moves in a straight line on a frictionless, horizontal surface. At one point in its path, its speed is 4.00 m/s; after it has traveled 2.50 m beyond this point, its speed is 6.00 m/s. Use the work\(-\)energy theorem to find the force acting on the sled, assuming that this force is constant and that it acts in the direction of the sled's motion.
Short Answer
Step by step solution
Identify the Known Parameters
Apply the Work-Energy Theorem
Calculate the Change in Kinetic Energy
Relate Work Done to Force
Conclusion
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Understanding Kinetic Energy
Applying this formula to the sled, we calculate its initial kinetic energy at a speed of 4.00 m/s and its final kinetic energy at 6.00 m/s.
- Initial kinetic energy: \( KE_i = \frac{1}{2} \times 12.00 \times (4.00)^2 = 96.00 \text{ J} \)
- Final kinetic energy: \( KE_f = \frac{1}{2} \times 12.00 \times (6.00)^2 = 216.00 \text{ J} \)
The Role of Constant Force
This constant force acts on the sled over a distance of 2.50 meters. According to the work-energy theorem, the work done by this force equals the change in kinetic energy.
- Total work done \( W = 120.00 \text{ J} \), which is calculated from the change in kinetic energy.
Exploring Sled Motion
In this exercise, the sled moves in a straight line and undergoes an increase in speed due to a constant force exerted over a certain distance.
Key elements of sled motion include:
- Direction of motion: The force is applied in the same direction as the sled's movement, making it easier to calculate its effect on speed.
- Acceleration: The increase in speed from 4.00 m/s to 6.00 m/s signifies acceleration, which is a change in velocity over time.
The Implications of a Frictionless Surface
On a frictionless surface:
- There is no opposing force to slow the sled down. This focus allows us to concentrate on the effects of the constant force.
- The only force that influences the sled’s acceleration is the external constant force applied.