please i need help with this question.
Initailly at rest, a car (mass=1300kg) accelerates north from a set of traffic lights at a constant rate for 10s. 11s after starting to accelerate it crosses an intersection and is hit by a second car (mass=1224kg) heading west at 65k/h. The two cars stick together and slide of across the intersection at 32km/h. How much energy was transformed into heat or sound in the collision and how much impulse did the engine of the first car provide while it was accelerating?
O.K. GREETINGS
To solve this problem, we need to calculate the energy transformed into heat or sound during the collision and the impulse provided by the engine of the first car while it was accelerating.
First, let's find the velocity of the first car when it crosses the intersection:
Using the equation of motion: v = u + at
Here, u = 0 (initial velocity), a = acceleration, and t = time.
Given that the car accelerates at a constant rate for 10 seconds, we can calculate the acceleration using the formula: a = (final velocity - initial velocity) / time.
Since the car starts from rest, the initial velocity is 0, and the final velocity is unknown. But we know the mass of the first car, so we can use the formula: F = ma, where F is the force applied by the engine.
Rearranging the formula, we have: a = F / m (acceleration is equal to force divided by mass).
To find the force, we need to calculate the impulse provided by the engine.
The impulse provided by the engine is given by the formula: Impulse = Force * time.
We can rearrange it as: Force = Impulse / time.
From the information given, we know that the engine provided an impulse for 10 seconds.
Using the equation for impulse, we have: Force = Impulse / time = F / m = m * acceleration / time.
Now, let's calculate the impulse provided by the engine:
Impulse = Force * time = (mass of the first car) * acceleration * time.
Once we have the impulse, we can calculate the velocity of the first car at the intersection using the equation: v = u + at.
In this case, the initial velocity (u) is 0, acceleration (a) is the constant rate of acceleration, given time (t) is 10 seconds.
Next, we need to find the velocity of the second car when it crosses the intersection.
Given that the second car is traveling horizontally (west) at a speed of 65 km/h, we can convert it to m/s by dividing by 3.6 (since 1 km/h = 1000 m / 3600 s = 1/3.6 m/s).
Now, we can calculate the velocity of the cars together after the collision.
Since the cars stick together and slide off across the intersection, the combined momentum before and after the collision remains the same.
Before the collision, the momentum of the first car is given by: momentum1 = (mass of the first car) * (velocity of the first car at the intersection).
The momentum of the second car is given by: momentum2 = (mass of the second car) * (velocity of the second car before the collision).
After the collision, the cars stick together and slide off, so the momentum is given by the formula: (mass of the combination) * (velocity of the combination after the collision).
We can equate the momentum before and after the collision and solve for the velocity of the combination after the collision.
The kinetic energy of the cars before the collision is given by: KE1 = (1/2) * (mass of the first car) * (velocity of the first car at the intersection)^2 + (1/2) * (mass of the second car) * (velocity of the second car before the collision)^2.
The kinetic energy of the cars after the collision is given by: KE2 = (1/2) * (mass of the combination) * (velocity of the combination after the collision)^2.
The difference in kinetic energy before and after the collision is the energy transformed into heat or sound:
Energy transformed = KE1 - KE2.
Using these formulas and the given values, you can now calculate the energy transformed into heat or sound in the collision and the impulse provided by the engine of the first car.