I need help with ONE PROBLEM
but it's really long.
Can some please Look at it, and help me out?
A Family is at the ice rink, trying out ice skating. Mother has a mass of 65kg, father has a mass of 85kg, and the twins, who are seven years old, each have a mass of 23kg, and all of them are wearing ice skates and standing on the ice.
Starting with everyone at rest, the father pushes the twins(Who are holding hands) with a constant force of magnitude 90N toward the mother. Father begins pushing when the twins are right in front of him, negligibly far away. He pushes until his arms are out straight, which is a distance of about 1m. The twins then continue with constant velocity for a distance of 3m until they reach the mother who catches and hugs them (this catching/hugging process is essentially a collision that lasts .6s)
1) Your task is to track the velocity, momentum and kinetic energy of the father, the twins and the mother. (You can treat the twins as a single "particle"
2) Consider four useful states for this situation and three processes that take place between the pairs of states. Define each state and process
a) State 1:_____________________________
b) Process 1->2:________________________
c) State 2:_____________________________
d) Process 2->3:_______________________
e) State 3:____________________________
f) Process 3->4:_______________________
g) State 4:____________________________
3) Make a sketch that shows each member of the family (as particles), the origin of coordinates and the positive direction.
HELP PLEASE
THANK YOU IN ADVANCE.
To help you with this problem, let's break it down into smaller steps.
Step 1: Calculate the acceleration of the twins
Since the force acting on the twins is constant and their mass is known, we can use Newton's second law (F = ma) to find the acceleration of the twins. The force applied by the father is 90N, and the combined mass of the twins is 23kg + 23kg = 46kg. Therefore, the acceleration (a) is given by a = F/m.
Step 2: Calculate the initial velocity of the twins
The twins start from rest, so their initial velocity (v_0) is 0 m/s.
Step 3: Calculate the final velocity of the twins
Using the equation of motion v^2 = v_0^2 + 2as, where v is the final velocity of the twins, v_0 is the initial velocity (0 m/s), a is the acceleration calculated in Step 1, and s is the distance the twins traveled (1m), we can find their final velocity.
Step 4: Calculate the momentum of the twins
The momentum (p) of an object is given by its mass (m) multiplied by its velocity (v). Since the twins are considered as a single "particle," their momentum (p_twins) is the product of their combined mass and their final velocity.
Step 5: Calculate the kinetic energy of the twins
The kinetic energy (KE) of an object is given by the formula KE = (1/2)mv^2, where m is the mass and v is the velocity. Using the combined mass of the twins and their final velocity, we can calculate their kinetic energy.
Step 6: Repeat Steps 1-5 for the father and the mother
You can follow the same steps to calculate the acceleration, initial velocity, final velocity, momentum, and kinetic energy of the father and the mother. The only difference is their individual masses.
For Step 2, since the father and mother are at rest initially, their initial velocities will also be 0 m/s. For Step 3, calculate the final velocities of the father and the mother based on the given distances. Finally, calculate the momentum and kinetic energy for each of them using their individual masses and final velocities.
For the sketch in Step 3, draw a coordinate system with the origin marked. Represent each member of the family (twins, father, and mother) as particles at appropriate positions on the ice rink. Also, indicate the positive direction on the coordinate axis.
By following these steps, you should be able to track the velocity, momentum, and kinetic energy of each family member at different stages of the problem.