Object A has of mass 7.20 kilograms, and object B has a mass of 5.75 kilograms. The two objects move along a straight line toward each other with velocities +2.00 meters/second and -1.30 meters/second respectively. What is the total kinetic energy of the objects after the collision, if the collision is perfectly elastic?
Bob
To find the total kinetic energy of the objects after the collision, we need to calculate the initial kinetic energy of each object and then sum them up.
The formula for kinetic energy is given by:
Kinetic Energy = (1/2) * mass * velocity^2
For object A:
Mass of A = 7.20 kilograms
Velocity of A = +2.00 meters/second
Kinetic Energy of A = (1/2) * 7.20 * (2.00)^2
= 14.40 joules
For object B:
Mass of B = 5.75 kilograms
Velocity of B = -1.30 meters/second
Kinetic Energy of B = (1/2) * 5.75 * (-1.30)^2
= 5.40 joules
Now, to find the total kinetic energy after the collision, we simply add up the kinetic energies of both objects.
Total Kinetic Energy = Kinetic Energy of A + Kinetic Energy of B
= 14.40 joules + 5.40 joules
= 19.80 joules
Therefore, the total kinetic energy of the objects after the collision, if the collision is perfectly elastic, is 19.80 joules.
To find the total kinetic energy of the objects after the collision, we first need to calculate the initial kinetic energies of the two objects.
The kinetic energy of an object can be calculated using the formula: KE = 1/2 * m * v^2, where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.
For object A:
Mass (m1) = 7.20 kg
Velocity (v1) = +2.00 m/s
Applying the formula, the kinetic energy of object A is:
KE1 = 1/2 * 7.20 kg * (2.00 m/s)^2
KE1 = 1/2 * 7.20 kg * 4.00 m^2/s^2
KE1 = 14.40 joules
For object B:
Mass (m2) = 5.75 kg
Velocity (v2) = -1.30 m/s
Using the formula, the kinetic energy of object B is:
KE2 = 1/2 * 5.75 kg * (-1.30 m/s)^2
KE2 = 1/2 * 5.75 kg * 1.69 m^2/s^2
KE2 = 4.86 joules
Next, since the collision is perfectly elastic, the kinetic energy is conserved. So the total kinetic energy after the collision would be the sum of the kinetic energies of object A and object B.
Total Kinetic Energy after collision = KE1 + KE2
Total Kinetic Energy after collision = 14.40 joules + 4.86 joules
Total Kinetic Energy after collision = 19.26 joules
Therefore, the total kinetic energy of the objects after the collision, if the collision is perfectly elastic, is 19.26 joules.
perfectly elastic means no energy lost in the collision
KE = 1/2 {[7.20 kg * (2.00 m/s)^2] + [5.75 kg * (1.30 m/s)^2]}