A 1000·kg car traveling with a velocity of 13·m/s north collides head-on with a 2000·kg truck traveling with a velocity of 17·m/s south. Immediately after the collision, the velocity of the car is 11·m/s south. Taking north as the positive direction, what is the velocity of the truck immediately after the collision?
conservation of momentum:
momentum before= momentum after
N means North, S means South, and N=-S
1000*13N+2000*17S=1000*11S+2000*V
13000N+34000(-N)=11000(-N)+2000V
do a little algebra, and solve for V
In my head, I get
V= (11000-21000)N/2000= 10m/s S
check that
Thank you sooo much!!! I wasn't dividing by the right number!
can you also explain how to find the impulse of this problem?
A large truck with a mass of 6500·kg and going 20·m/s east collides with a car whose mass is 1100·kg and which is at rest. If the impulse exerted on the car by the truck is 12000·N·s east, find the impulse exerted by the car on the truck. Take east as the postive direction
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
Let's calculate the momentum of the car and the truck before the collision separately.
The momentum of an object is given by the product of its mass (m) and its velocity (v).
The momentum (p) is calculated using the formula:
p = m * v
Let's calculate the momentum of the car before the collision:
Mass of the car (m1) = 1000 kg
Velocity of the car (v1) = 13 m/s
Momentum of the car before the collision (p1) = m1 * v1
p1 = 1000 kg * 13 m/s
p1 = 13,000 kg·m/s (North)
Similarly, let's calculate the momentum of the truck before the collision:
Mass of the truck (m2) = 2000 kg
Velocity of the truck (v2) = -17 m/s (since it is south, we take negative velocity)
Momentum of the truck before the collision (p2) = m2 * v2
p2 = 2000 kg * (-17 m/s)
p2 = -34,000 kg·m/s (South)
Now, let's calculate the momentum after the collision.
The equation for conservation of momentum can be written as:
p1 + p2 = p1' + p2'
Where p1' and p2' represent the momentums of the car and the truck immediately after the collision, respectively.
Given that the velocity of the car immediately after the collision is 11 m/s (South), we can calculate its momentum:
Mass of the car (m1') = 1000 kg
Velocity of the car (v1') = -11 m/s (South)
Momentum of the car after the collision (p1') = m1' * v1'
p1' = 1000 kg * (-11 m/s)
p1' = -11,000 kg·m/s (South)
Now, let's substitute the values into the conservation of momentum equation to solve for the momentum of the truck after the collision:
13,000 kg·m/s (North) + (-34,000 kg·m/s (South)) = -11,000 kg·m/s (South) + p2'
Subtracting 13,000 kg·m/s (North) from both sides:
-34,000 kg·m/s (South) = -11,000 kg·m/s (South) + p2' - 13,000 kg·m/s (North)
Combining the South terms on the right side:
-34,000 kg·m/s - (-11,000 kg·m/s) = p2' - 13,000 kg·m/s
Simplifying the left side:
-34,000 kg·m/s + 11,000 kg·m/s = p2' - 13,000 kg·m/s
-23,000 kg·m/s = p2' - 13,000 kg·m/s
Adding 13,000 kg·m/s to both sides:
-23,000 kg·m/s + 13,000 kg·m/s = p2'
-10,000 kg·m/s = p2'
Therefore, the momentum of the truck immediately after the collision is -10,000 kg·m/s. The negative sign indicates that the truck is still traveling south.
To find the velocity of the truck immediately after the collision, we can divide its momentum by its mass:
Momentum of the truck after the collision (p2') = -10,000 kg·m/s
Mass of the truck (m2) = 2000 kg
Velocity of the truck after the collision (v2') = p2' / m2
v2' = (-10,000 kg·m/s) / (2000 kg)
v2' = -5 m/s
Therefore, the velocity of the truck immediately after the collision is 5 m/s in the south direction.
To solve this problem, we can use the principles of conservation of momentum and apply them to the collision between the car and the truck.
The principle of conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision, provided no external forces are acting on the system.
Let's define the positive direction as north and the negative direction as south. We can calculate the total momentum before the collision using the formula:
Total momentum before = (mass of car * velocity of car) + (mass of truck * velocity of truck)
Given:
Mass of car (m1) = 1000 kg
Velocity of car (v1) = 13 m/s north
Mass of truck (m2) = 2000 kg
Velocity of truck (v2) = 17 m/s south
Total momentum before = (1000 kg * 13 m/s) + (2000 kg * (-17 m/s)) [Note: we consider the opposite direction as negative]
Total momentum before = (13000 kg·m/s) + (-34000 kg·m/s) = -21000 kg·m/s
Now, let's calculate the total momentum after the collision using the formula:
Total momentum after = (mass of car * velocity of car) + (mass of truck * velocity of truck)
Given:
Velocity of car after collision (v1') = 11 m/s south
Velocity of truck after collision (v2') = ?
Total momentum after = (1000 kg * (-11 m/s)) + (2000 kg * v2')
Total momentum after = -11000 kg·m/s + 2000 kg·m/s * v2'
Since the total momentum before the collision is equal to the total momentum after the collision, we can equate the two equations:
-21000 kg·m/s = -11000 kg·m/s + 2000 kg·m/s * v2'
Simplifying the equation, we get:
10000 kg·m/s = 2000 kg·m/s * v2'
Dividing both sides of the equation by 2000 kg·m/s, we get:
v2' = 5 m/s
Therefore, the velocity of the truck immediately after the collision is 5 m/s south.