A 31.0 kg child on a swing reaches a maximum height of 1.92 m above their rest position.
Assuming no loss of energy:
a) At what point during the swing will she attain their maximum speed?
b) What will be her maximum speed through the subsequent swing?
c) Assuming this maximum height was the result of one push from her parent, what was the
I found these questions online for a test and I'm unsure how to go about these questions. Thankfully, I have one week to prepare. I need help
Sure! I can help you with these physics questions step-by-step. Let's break down each question and solve them one by one:
a) To find out at what point during the swing the child will attain their maximum speed, we need to understand the concept of conservation of energy. At the highest point of the swing, all the potential energy is converted into kinetic energy.
The potential energy (PE) of an object with mass (m) at a certain height (h) is given by the formula:
PE = m * g * h
Where:
m = mass of the object (31.0 kg in this case)
g = acceleration due to gravity (9.8 m/s²)
h = height above the rest position (1.92 m)
At the maximum height, all potential energy is converted into kinetic energy (KE).
Therefore, we can equate PE to KE:
PE = KE
Substituting the formulas:
m * g * h = (1/2) * m * v^2
Where:
v = velocity of the swing at the maximum point (which is the speed we are looking for)
We can simplify the equation and solve for v:
v = sqrt(2 * g * h)
Plug in the values:
v = sqrt(2 * 9.8 m/s² * 1.92 m)
v = sqrt(37.632) m/s
v ≈ 6.13 m/s
Therefore, the child will attain their maximum speed of approximately 6.13 m/s at the highest point of the swing.
b) To find the maximum speed through the subsequent swing, we need to consider the conservation of mechanical energy. In a negligibly lossless system, the total mechanical energy remains constant.
The mechanical energy (ME) of the system is the sum of potential energy (PE) and kinetic energy (KE):
ME = PE + KE
Since there are no energy losses, the mechanical energy at the highest point of the swing is the same as at the lowest point of the swing. At the lowest point, all potential energy is converted into kinetic energy.
So, using the formulas from the previous question:
ME at highest point = m * g * h = 31.0 kg * 9.8 m/s² * 1.92 m
ME at lowest point = (1/2) * m * v^2
We can equate these two expressions and solve for v:
31.0 kg * 9.8 m/s² * 1.92 m = (1/2) * 31.0 kg * v^2
Simplifying and solving for v:
v^2 = (31.0 kg * 9.8 m/s² * 1.92 m) / (1/2) * 31.0 kg
v^2 = 9.8 m/s² * 1.92 m * 2
v^2 = 37.632 m²/s²
Taking the square root:
v = sqrt(37.632) m/s
v ≈ 6.13 m/s
Therefore, the child's maximum speed through the subsequent swing is also approximately 6.13 m/s.
c) Unfortunately, you didn't provide enough information to calculate the force exerted by the parent's push. We would need additional data such as the distance over which the parent applied the force or the time it took to reach the maximum height.
I hope this helps you understand and solve these questions. Let me know if you have any further queries!
Sure! I'm here to help. Let's go through each question step by step.
a) To determine at what point during the swing the child will attain their maximum speed, we need to consider the principle of conservation of mechanical energy. The maximum speed occurs at the lowest point of the swing, where all of the potential energy is converted into kinetic energy.
To calculate the maximum speed (v) of the child, we can use the formula for kinetic energy:
Kinetic Energy = (1/2) * mass * velocity^2
Since the child reaches a maximum height of 1.92 m above their rest position, we can calculate the potential energy (PE) at that position using the equation:
Potential Energy = mass * acceleration due to gravity * height
Setting the potential energy equal to the kinetic energy, we have:
Kinetic Energy = Potential Energy
(1/2) * mass * velocity^2 = mass * acceleration due to gravity * height
Simplifying the equation, we get:
(1/2) * velocity^2 = acceleration due to gravity * height
We know the value for the height (1.92 m) and the acceleration due to gravity (approximately 9.8 m/s^2). By substituting these values into the equation, we can solve for the velocity (v).
b) Once we've determined the maximum speed at the lowest point of the swing, we can use this velocity to answer the second question. The maximum speed will remain constant throughout the subsequent swing as there is no loss of energy mentioned.
c) To determine what kind of force the parent applied during the push, we need to calculate the work done by the parent.
The work done is equal to the change in potential energy, which can be calculated using the formula:
Work = force * distance * cos(theta)
Here, force is the force applied by the parent, distance is the displacement of the swing, and theta is the angle between the force and the displacement. Since the swing goes from the rest position to the maximum height (1.92 m), the displacement is equal to the height.
Knowing the work done and that work is equal to the force multiplied by the distance, we can calculate the force applied by the parent.
Remember to use the appropriate units (e.g., meters, kilograms, seconds) and to double-check your calculations.
I hope this explanation helps you to understand how to approach these questions. Good luck with your test preparation! If you have any further questions, feel free to ask.
2.At the bottom of her her gravitational potential energy is
h = 0 so GPE = 0
3.At the bottom of her swing her kinetic energy is
max KE = max GPE = 584 J
4.the point during the swing where she attain her maximum speed was at the bottom
max KE
5. her maximum speed will be?
max KE = max GPE
1/2 31.0 v2 = 584 J
v2 = 37.67
v = 6.14 m/s