A 1500 kg car moving east at 15 m/s collides with a 1730 kg car moving south at 15 m/s and the two cars stick together. What is the velocity of the cars right after the collision?
How much kinetic energy was converted to another form during the collision?
Momentum, a vector, is conserved. Work conservation of momentum in E, and then in S directions.
To find the velocity of the cars right after the collision, we can apply the principles of conservation of momentum. The law of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision, provided there are no external forces.
The momentum of an object is given by the product of its mass and velocity (p = mv).
Given:
Mass of car 1 (m1) = 1500 kg
Velocity of car 1 (v1) = 15 m/s (moving east)
Mass of car 2 (m2) = 1730 kg
Velocity of car 2 (v2) = 15 m/s (moving south)
The total momentum before the collision can be calculated by summing the individual momenta of the two cars:
p(before) = p1 + p2
= (m1 * v1) + (m2 * v2)
We can substitute the given values into the equation:
p(before) = (1500 kg * 15 m/s) + (1730 kg * 15 m/s)
Next, we need to determine the velocity of the cars right after the collision (v(after)). Since the two cars stick together, we can assume they move as a single combined mass after the collision.
We can set up an equation using the principle of conservation of momentum:
p(before) = p(after)
(m1 * v1) + (m2 * v2) = (m * v(after))
Substituting the given values:
(1500 kg * 15 m/s) + (1730 kg * 15 m/s) = (m * v(after))
Solving for v(after):
(1500 kg * 15 m/s) + (1730 kg * 15 m/s) = (3230 kg * v(after))
(22500 kg·m/s) + (25950 kg·m/s) = (3230 kg * v(after))
48450 kg·m/s = (3230 kg * v(after))
v(after) = 48450 kg·m/s / 3230 kg
v(after) = 15 m/s
Therefore, the velocity of the cars right after the collision is 15 m/s.
To determine the amount of kinetic energy converted to another form during the collision, we can calculate the total kinetic energy before and after the collision and find the difference.
The kinetic energy of an object is given by the equation: KE = 0.5 * m * v^2
Let's calculate the total initial kinetic energy (KE(before)):
KE(before) = 0.5 * (m1 * v1^2) + 0.5 * (m2 * v2^2)
= 0.5 * (1500 kg) * (15 m/s)^2 + 0.5 * (1730 kg) * (15 m/s)^2
Next, we can calculate the total final kinetic energy (KE(after)):
KE(after) = 0.5 * (m * v(after)^2)
= 0.5 * (3230 kg) * (15 m/s)^2
Finally, we can compute the difference between the initial and final kinetic energy to determine the amount converted to another form:
Kinetic energy converted = KE(before) - KE(after)
Substitute the values and evaluate the expression:
Kinetic energy converted = (0.5 * (1500 kg) * (15 m/s)^2 + 0.5 * (1730 kg) * (15 m/s)^2) - (0.5 * (3230 kg) * (15 m/s)^2)
By calculating the expression, you will get the amount of kinetic energy converted during the collision.