You and your friends are doing physics experiments on a frozenpond that serves as a frictionless, horizontal surface. Sam,with mass 80.0 kg, is given a push and slides eastward. Abigail, with mass 50.0 kg, is sent sliding northward. Theycollide and after the collision, Sam is moving at 37.0degrees north of east with a speed of 6.00 m/s and Abigail ismoving at an angle β=23.0 degrees south of east with a speedof 9.00 m/s.
By how much did the total kinetic energy of the two peopledecrease during the collision?
To find the change in kinetic energy during the collision, we first need to calculate the initial and final kinetic energies of Sam and Abigail.
The initial kinetic energy of an object is given by the formula: KE = (1/2) * mass * velocity^2
For Sam, with a mass of 80.0 kg and a speed of 6.00 m/s:
Initial KE of Sam = (1/2) * 80.0 kg * (6.00 m/s)^2
For Abigail, with a mass of 50.0 kg and a speed of 9.00 m/s:
Initial KE of Abigail = (1/2) * 50.0 kg * (9.00 m/s)^2
Next, we can calculate the final kinetic energies of Sam and Abigail after the collision using their respective speeds and angles.
The final kinetic energy of an object is given by the formula: KE = (1/2) * mass * velocity^2
For Sam, with a speed of 6.00 m/s at an angle of 37.0 degrees north of east:
Final KE of Sam = (1/2) * 80.0 kg * (6.00 m/s)^2
For Abigail, with a speed of 9.00 m/s at an angle of 23.0 degrees south of east:
Final KE of Abigail = (1/2) * 50.0 kg * (9.00 m/s)^2
Now, we can calculate the change in kinetic energy by subtracting the final kinetic energy from the initial kinetic energy for each person.
Change in KE for Sam = Initial KE of Sam - Final KE of Sam
Change in KE for Abigail = Initial KE of Abigail - Final KE of Abigail
Finally, we can find the total change in kinetic energy by summing up the individual changes in kinetic energy:
Total change in kinetic energy = Change in KE for Sam + Change in KE for Abigail
Substitute the given values into the formulas above to calculate the answer.