A 68.0 kg boy and his 45.0 kg sister, both wearing roller blades face each other at rest. The girl pushes the boy hard, sending him backward with a velocity 3.70 m/s toward the west. Ignore friction.
How much chemical energy is converted into mechanical energy in the girl's muscles?
whenever i figure the answer i get 720 but htis is not right.
What you want is the total kinetic energy of BOTH of the skaters after she pushes him. Because they are on skates, and total momentum is conserved, she scquires the same momentum as her brother, but in the opposite direction.
Her own velocity will be 68*3.7/45 = 5.59 m/s after the push, in order for her to have the same momentum. Add her kinetic energy to his.
His is 465.5 J
Hers is 703.1 J
Add them. I don't see how you got 720.
To calculate the amount of chemical energy converted into mechanical energy in the girl's muscles, we can use the principle of conservation of momentum.
First, let's determine the initial momentum and final momentum of the system.
Given:
Mass of the boy (mb) = 68.0 kg
Mass of the girl (mg) = 45.0 kg
Initial velocity of the boy (vb initial) = 0 m/s (since he is at rest)
Final velocity of the boy (vb final) = -3.70 m/s (toward the west)
The initial momentum of the system can be calculated as:
Initial momentum = (Mass of the boy * Initial velocity of the boy) + (Mass of the girl * Initial velocity of the girl)
Initial momentum = (68.0 kg * 0 m/s) + (45.0 kg * 0 m/s) = 0 kg*m/s
The final momentum of the system can be calculated as:
Final momentum = (Mass of the boy * Final velocity of the boy) + (Mass of the girl * Final velocity of the girl)
Final momentum = (68.0 kg * -3.70 m/s) + (45.0 kg * 0 m/s) = -251.6 kg*m/s
Now, the change in momentum can be calculated as:
Change in momentum = Final momentum - Initial momentum
Change in momentum = -251.6 kg*m/s - 0 kg*m/s = -251.6 kg*m/s
According to the law of conservation of momentum, the change in momentum of the boy should be equal in magnitude but opposite in direction to the change in momentum of the girl.
Therefore, the change in momentum of the girl would be +251.6 kg*m/s.
Now, let's calculate the amount of energy converted from chemical energy into mechanical energy in the girl's muscles.
To calculate the energy, we can use the formula:
Mechanical Energy = Change in momentum * Final velocity of the girl
Given:
Change in momentum of the girl = +251.6 kg*m/s
Final velocity of the girl (vg final) = 0 m/s (since she is also at rest after pushing)
Mechanical Energy = (+251.6 kg*m/s * 0 m/s) = 0 Joules
Therefore, the amount of chemical energy converted into mechanical energy in the girl's muscles is 0 Joules.