Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1500 kg and was approaching at 9.00 m/s due south. The second car has a mass of 700 kg and was approaching at 15.0 m/s due west.
(a) Calculate the final velocity of the cars.
(b) How much kinetic energy is lost in the collision? (This energy goes into deformation of the cars.)
To solve this problem, we can apply the principles of conservation of momentum and conservation of kinetic energy.
(a) To calculate the final velocity of the cars, we need to find their combined momentum and divide it by their combined mass.
Step 1: Calculate the momentum of each car.
The momentum of an object is given by the product of its mass and velocity.
Momentum of the first car (m1v1) = (1500 kg) * (9.00 m/s)
Momentum of the second car (m2v2) = (700 kg) * (-15.0 m/s) [The negative sign indicates the opposite direction]
Step 2: Find the total momentum of the cars.
Total momentum before the collision = m1v1 + m2v2
Total momentum before the collision = (1500 kg) * (9.00 m/s) + (700 kg) * (-15.0 m/s)
Step 3: Find the combined mass of the two cars.
Combined mass = m1 + m2
Combined mass = 1500 kg + 700 kg
Step 4: Calculate the final velocity of the cars.
Final velocity = Total momentum before the collision / Combined mass
(b) To calculate the kinetic energy lost in the collision, we need to find the kinetic energy before the collision and subtract the kinetic energy after the collision.
Step 1: Calculate the initial kinetic energy of each car.
Kinetic energy is given by the formula: KE = (1/2) * m * v^2
Initial kinetic energy of the first car = (1/2) * (1500 kg) * (9.00 m/s)^2
Initial kinetic energy of the second car = (1/2) * (700 kg) * (15.0 m/s)^2
Step 2: Calculate the total initial kinetic energy of the cars.
Total initial kinetic energy = Initial kinetic energy of the first car + Initial kinetic energy of the second car
Step 3: Calculate the final kinetic energy of each car.
Final kinetic energy is given by the formula: KE = (1/2) * m * v^2
Final kinetic energy of the first car = (1/2) * (1500 kg) * (final velocity)^2
Final kinetic energy of the second car = (1/2) * (700 kg) * (final velocity)^2
Step 4: Calculate the total final kinetic energy of the cars.
Total final kinetic energy = Final kinetic energy of the first car + Final kinetic energy of the second car
Step 5: Calculate the kinetic energy lost in the collision.
Kinetic energy lost = Total initial kinetic energy - Total final kinetic energy
Note: Since values were not provided for the final velocity, they will be calculated based on the steps above.
To calculate the final velocity of the cars, we can apply the principles of conservation of linear momentum. The total momentum before the collision is equal to the total momentum after the collision.
(a) First, we need to determine the initial momentum of each car.
Momentum (p) = mass (m) x velocity (v)
For the first car:
Mass of the first car (m1) = 1500 kg
Velocity of the first car (v1) = 9.00 m/s (south)
Momentum of the first car (p1) = m1 x v1
For the second car:
Mass of the second car (m2) = 700 kg
Velocity of the second car (v2) = 15.0 m/s (west)
Momentum of the second car (p2) = m2 x v2
Now that we have the initial momentum of each car, we can calculate the total momentum before the collision.
Total momentum before the collision (p_initial) = p1 + p2
After the collision, the two cars stick together and move in one direction. Let's assume their final velocity is v_final. So, the total momentum after the collision (p_final) is given by:
Total momentum after the collision (p_final) = (m1 + m2) x v_final
According to the principle of conservation of momentum, the total momentum before the collision (p_initial) is equal to the total momentum after the collision (p_final). Therefore:
p_initial = p_final
p1 + p2 = (m1 + m2) x v_final
Substituting the values:
(m1 x v1) + (m2 x v2) = (m1 + m2) x v_final
Now, we can solve for the final velocity (v_final).
Let's substitute the given values:
m1 = 1500 kg
v1 = 9.00 m/s
m2 = 700 kg
v2 = 15.0 m/s
Using these values, we can calculate the final velocity.
(b) To calculate the amount of kinetic energy lost in the collision, we need to find the difference in the initial total kinetic energy and the final total kinetic energy.
The kinetic energy (K) of an object is given by the formula:
Kinetic energy (K) = 1/2 x mass (m) x velocity^2 (v^2)
The initial kinetic energy of the first car (K1_initial) = 1/2 x m1 x v1^2
The initial kinetic energy of the second car (K2_initial) = 1/2 x m2 x v2^2
The initial total kinetic energy (K_initial) = K1_initial + K2_initial
The final kinetic energy (K_final) = 1/2 x (m1 + m2) x v_final^2
The kinetic energy lost in the collision = K_initial - K_final
Substituting the given values, we can calculate the amount of kinetic energy lost in the collision.
No Damon, he meant moving due south. negative on y axis.
You can't use conservation of momentum since it's 2d from what MY book told me.
Use the components of Velocity vectors.
m1v1+m2v2=Vx (m1+m2)
m1v1+m2v2=Vy (m1 +m2)
Vf= sq.rt.(Vx^2 + Vy^2)
theta= arctan(Vy/Vx)
I assume you mean approaching FROM south for example, so moving north
momentum 1500 * 9 N = 13500 N
momentum 700 * 15 E = 10500 E
final mass = 1500 + 700 = 2200
2200 v cos (heading ) = 13500
2200 v sin (heading)= 10500
tan heading = 10500/13500
heading = 37.9 degrees east of north
2200 v cos (37.9) = 13500
so
v = 7.77 m/s
initial ke = (1/2) 1500 (81) + (1/2) 700 (225)
final ke = (1/2) 2200 (7.77)^2
subtract