A 1200kg travelling east collides with another 1000kg car travelling north. If they are both travelling at 90km/h and the collision is completely inelastic, find the velocity of the systemafter collision.
To find the velocity of the system after the collision, we can first calculate the total momentum before the collision and then use that to find the velocity.
Momentum, denoted as p, is a vector quantity defined as the product of an object's mass and velocity. The momentum of an object can be calculated using the formula p = m * v, where m is the mass and v is the velocity of the object.
1. Convert the mass and velocity from km/h to m/s:
The mass of the car travelling east is 1200 kg and the mass of the car travelling north is 1000 kg. The velocity of both cars is 90 km/h.
To convert the velocity from km/h to m/s, we divide by 3.6 since 1 km/h = 1/3.6 m/s:
Velocity of both cars = 90 km/h ÷ 3.6 = 25 m/s.
2. Calculate the momentum of each car before the collision:
Momentum of the car travelling east = mass * velocity = 1200 kg * 25 m/s = 30,000 kg·m/s (east)
Momentum of the car travelling north = mass * velocity = 1000 kg * 25 m/s = 25,000 kg·m/s (north)
3. Add the momenta of both cars to find the total momentum before the collision:
Total momentum before the collision = Momentum of the car going east + Momentum of the car going north
= 30,000 kg·m/s (east) + 25,000 kg·m/s (north)
To combine the two momenta, we need to treat them as vectors. Since momentum is a vector, we would need to use vector addition to combine them. In vector addition, we can treat east as the positive x-direction and north as the positive y-direction. Therefore, the total momentum can be obtained using vector addition.
4. Calculate the total momentum using vector addition:
Total momentum = sqrt((30,000)^2 + (25,000)^2) = sqrt(1,200,000,000) ≈ 34,641.02 kg·m/s
The direction of the momentum is given by the vector sum of the individual momenta. To find the angle θ, we can use trigonometry:
θ = arctan(25,000 kg·m/s ÷ 30,000 kg·m/s) ≈ 0.7071 rad
5. Use the total momentum to find the velocity of the system after the collision:
Since the collision is completely inelastic, the two cars will stick together after the collision and move as one system.
The velocity of the system after the collision is the total momentum divided by the combined mass of both cars.
Combined mass = mass of the car travelling east + mass of the car travelling north = 1200 kg + 1000 kg = 2200 kg
Velocity of the system after collision = Total momentum ÷ Combined mass
Velocity of the system after collision = 34,641.02 kg·m/s ÷ 2200 kg ≈ 15.75 m/s (θ degrees)
Therefore, the velocity of the system after the collision is approximately 15.75 m/s at an angle of 0.7071 radians (θ degrees) to the east.
the final mass is 2200 Kg if it is totally inelastic and they stick to each other.
east momentum
1200 * 90 = 2200 Ve
north momentum
1000 * 90 = 2200 Vn
|V| = sqrt (Ve^2+Vn^2)
tan compass angle east of north = Ve/Vn