A Child Is Sliding On A Sled At 1.9 M/s To The Right. You Stop The Sled By Pushing On It For 0.80 S In A Direction Opposite To Its Motion. If The Mass Of The Child And Sled Is 38 Kg , What Is The Magnitude Of The Average Force You Need To Apply To Stop
Introduction
When a child is sliding on a sled, it's essential to understand the physics involved in stopping the sled safely. In this scenario, we have a child and a sled moving at a speed of 1.9 m/s to the right. To stop the sled, we need to apply a force in the opposite direction of its motion. In this article, we will calculate the magnitude of the average force required to stop the sled.
Understanding the Problem
To solve this problem, we need to apply the concept of impulse and momentum. The impulse-momentum theorem states that the impulse applied to an object is equal to the change in its momentum. Mathematically, this can be expressed as:
J = Δp
where J is the impulse, and Δp is the change in momentum.
Calculating the Initial Momentum
The initial momentum of the child and sled can be calculated using the formula:
p_i = m * v_i
where p_i is the initial momentum, m is the mass of the child and sled, and v_i is the initial velocity.
Given that the mass of the child and sled is 38 kg and the initial velocity is 1.9 m/s, we can calculate the initial momentum as follows:
p_i = 38 kg * 1.9 m/s = 72.2 kg m/s
Calculating the Final Momentum
Since the sled comes to rest after the force is applied, the final momentum is zero.
Calculating the Impulse
The impulse applied to the sled can be calculated using the formula:
J = Δp = p_f - p_i
where J is the impulse, and Δp is the change in momentum.
Since the final momentum is zero, the impulse can be calculated as:
J = 0 - 72.2 kg m/s = -72.2 kg m/s
Calculating the Average Force
The average force required to stop the sled can be calculated using the formula:
F_avg = J / Δt
where F_avg is the average force, J is the impulse, and Δt is the time over which the force is applied.
Given that the impulse is -72.2 kg m/s and the time over which the force is applied is 0.80 s, we can calculate the average force as follows:
F_avg = -72.2 kg m/s / 0.80 s = -90.25 N
Conclusion
In conclusion, to stop a child and sled moving at a speed of 1.9 m/s, we need to apply an average force of 90.25 N in the opposite direction of its motion. This calculation is based on the impulse-momentum theorem and takes into account the mass of the child and sled, as well as the time over which the force is applied.
Discussion
This problem highlights the importance of understanding the physics involved in stopping a moving object. By applying the concept of impulse and momentum, we can calculate the average force required to stop the sled safely. This calculation can be useful in various real-world scenarios, such as stopping a car or a train.
References
- Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.
- Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.
Additional Resources
- Khan Academy: Impulse and Momentum
- Physics Classroom: Impulse and Momentum
- MIT OpenCourseWare: Physics 8.01: Classical Mechanics
A Child on a Sled: Q&A =========================
Q: What is the relationship between impulse and momentum?
A: The impulse-momentum theorem states that the impulse applied to an object is equal to the change in its momentum. Mathematically, this can be expressed as:
J = Δp
where J is the impulse, and Δp is the change in momentum.
Q: How do you calculate the initial momentum of an object?
A: The initial momentum of an object can be calculated using the formula:
p_i = m * v_i
where p_i is the initial momentum, m is the mass of the object, and v_i is the initial velocity.
Q: What is the final momentum of an object when it comes to rest?
A: When an object comes to rest, its final momentum is zero.
Q: How do you calculate the impulse applied to an object?
A: The impulse applied to an object can be calculated using the formula:
J = Δp = p_f - p_i
where J is the impulse, and Δp is the change in momentum.
Q: What is the average force required to stop an object?
A: The average force required to stop an object can be calculated using the formula:
F_avg = J / Δt
where F_avg is the average force, J is the impulse, and Δt is the time over which the force is applied.
Q: What is the significance of the impulse-momentum theorem?
A: The impulse-momentum theorem is a fundamental concept in physics that helps us understand the relationship between impulse and momentum. It is used to calculate the average force required to stop an object, which is essential in various real-world scenarios.
Q: What are some real-world applications of the impulse-momentum theorem?
A: The impulse-momentum theorem has numerous real-world applications, including:
- Stopping a car or a train
- Calculating the force required to stop a moving object
- Understanding the physics of collisions
- Designing safety features for vehicles and equipment
Q: What are some common mistakes to avoid when calculating impulse and momentum?
A: Some common mistakes to avoid when calculating impulse and momentum include:
- Failing to consider the direction of the force and velocity
- Not accounting for the mass of the object
- Using the wrong formula or units
- Not considering the time over which the force is applied
Q: How can I practice calculating impulse and momentum?
A: You can practice calculating impulse and momentum by:
- Solving problems and exercises
- Using online resources and calculators
- Conducting experiments and simulations
- Joining online communities and forums to discuss physics-related topics
Conclusion
In conclusion, the impulse-momentum theorem is a fundamental concept in physics that helps us understand the relationship between impulse and momentum. By applying this theorem, we can calculate the average force required to stop an object, which is essential in various real-world scenarios. Remember to avoid common mistakes and practice calculating impulse and momentum to become proficient in this area of physics.