A father pulls his son, whose mass is 26.7 kg and who is sitting on a swing with ropes of length 3.27 m, backward until the ropes make an angle of 35.6° with respect to the vertical. He then releases his son from rest. What is the speed of the son at the bottom of the swinging motion?
I'm just wondering what formula I can use in order to find the answer
just did it below
kinetic energy at bottom = potential energy at top
Formula? You have to do some thinking.
draw the diagrem.
Calculate the height off ground the swing is at the start position:
L=3.27-3.27cos35.6
calculate the starting PEnergy
mass*g*startingHeight
Calculate velocity from
final KE=initial PE
1/2 mv^2=mgh
solve for v.
To find the speed of the son at the bottom of the swinging motion, you can use the conservation of mechanical energy.
The formula for the speed at the bottom of the swing is:
v = √(2*g*h)
Where:
- v is the speed at the bottom of the swing
- g is the acceleration due to gravity (approximately 9.8 m/s²)
- h is the height of the swing at the bottom of the motion
You can calculate the height, h, using the given information about the angle and length of the swing ropes.
The height, h, is equal to the vertical component of the displacement of the swing. It can be calculated as:
h = L * (1 - cosθ)
Where:
- L is the length of the swing ropes
- θ is the angle made by the ropes with respect to the vertical
Now that we know how to calculate h, we can substitute it back into the first formula to find the final answer.
Remember to convert any angles used in the calculations to radians if necessary.