Physics Assignment: Word Problem?
This is one of the toughest things I've ever had to work with in my Physics class. Please help me understand how to solve this.
A car traveling due east strikes a car traveling due north at and intersection, and the two move together as a unit. The eastward-moving car has a mass of 1300kg and a speed of 30 km/h. The northward-moving car has a mass of 1100kg and a speed of 20 km/h. he cars moved for 2.8s with uniform acceleration. (Momentum is a vector quantity so they can be added.)
Question 1: A property owner on the east corner of the intersection claims his fence was torn down in the collision. The fence is 12m from the street. Is he telling the truth or lying to get the insurance money? Use physics/math to justify your answer. You should include how far the cars move, the angle they move at, and the likelihood of them hitting the fence.
Question 2: Is this collision elastic or inelastic? you should include momentum and velocity data here.
Comments
Let's start by conserving momentum in each direction.
The only momentum in the eastward direction before the collision is from the first car. It's momentum is (1300 kg)(30 km/h)(1 h / 3600 s)( 1000 m / 1 km) = 10833 kg m/s
This momentum must be conserved after the collision. We can find the eastward velocity (Ve) of the two cars as:
10833 kg m/s = (1300 kg + 1100 kg)(Ve)
Ve = 4.514 m/s
The only momentum in the northerly direction before the collision is from the 2nd car. This momentum is: (1100 kg)(20 km/h)(1 hr / 3600 s)(1000 m / 1 km) = 6111 kg m/s
This momentum must also be conserved after the collision. We can find the northerly velocity of the two cars as:
6111 kg m/s = (1300 kg + 1100 kg)*(Vn)
Vn = 2.546 m/s
Question 1)
That property owner is on the eastern side and his fence is 12 m from the street. We need to use our calculated eastern velocity to see if the cars made it 12 m in the 2.8 s.
(4.514 m/s) * (2.8 s) = 12.64 m. It looks like they did travel far enough in the eastward direction to hit his fence.
They also traveled (2.546 m/s)(2.8 s) = 7.129 m in the northward direction after the collision. They will only have hit his fence if his fence extends this far in the northward direction.
The cars make an angle of arctan(2.546 / 4.514) = 29.4 deg north of east as they travel after the collision.
Question 2)
This collision is inelastic. Elastic collisions conserve kinetic energy. This one does not.
Initial kinetic energy: (1/2)(10833 kg m/s)^2 / (1300 kg) + (1/2)(6111 kg m/s)^2 / (1100 kg) = 62111 J
Final kinetic energy: (1/2)(1300 kg + 1100 kg)( (4.514 m/s)^2 + (2.546 m/s)^2) = 32230 J