A 2000 kg car is rolling at 2.0 m/s. You would like to stop the car by firing a 12 kg blob of sticky clay at it. How fast should you fire the clay?
i keep getting 25.8 but apparently that isn't right so i'm at a loss
This is an example of Conservation of Momentum. This means total momentum in the system is conserved. Put into an equation this is
p1initial + p2initial = p1final + p2final
Let's say that the car is obj 1
Minitial = 2000 kg
vinitial = 2.0 m/s
Mfinal = 2000 kg
Vfinal = 0 m/s(because it is stopped by the clay)
Obj 2 is the clay
Minitial = 12 kg
vinitial = 0 m/s
Mfinal = 12kg
Vfinal = ? m/s
so... knowing that p = m* v, and substituting the known values
2000kg * 2 m/s + 0 = 0 + 12kg * vfinal of clay
v final of clay = (2000kg*2m/s)/12kg
v = 333.3 m/s
To solve this problem, we can apply the principle of conservation of momentum. According to this principle, the initial momentum of the car and the clay should be equal to the final momentum after the collision.
The formula for momentum is given by: momentum (p) = mass (m) * velocity (v)
Initially, the momentum of the car is mass of the car (m1) * initial velocity of the car (v1), which can be written as: p1 = m1 * v1
Initially, the momentum of the clay is mass of the clay (m2) * initial velocity of the clay (v2), which can be written as: p2 = m2 * v2
Since the car and the clay are stuck together after the collision, the final velocity (vf) will be the same. Thus, the final momentum is (m1 + m2) * vf.
According to the principle of conservation of momentum, we have p1 + p2 = (m1 + m2) * vf
Substituting the given values:
m1 = 2000 kg (mass of the car)
v1 = 2.0 m/s (initial velocity of the car)
m2 = 12 kg (mass of the clay)
v2 = ? (initial velocity of the clay, what we need to find)
vf = ? (final velocity)
The equation becomes: (2000 kg * 2.0 m/s) + (12 kg * v2) = (2000 kg + 12 kg) * vf
Simplifying the equation further:
4000 kg•m/s + 12 kg•v2 = 2012 kg • vf
We need to solve for the initial velocity of the clay, v2. Rearranging the equation, we have:
12 kg•v2 = 2012 kg • vf - 4000 kg•m/s
Divide both sides by 12 kg:
v2 = (2012 kg • vf - 4000 kg•m/s) / 12 kg
Now, we need to find the final velocity, vf. We can use the principle of conservation of kinetic energy. The initial kinetic energy of the car is given by: KE1 = (1/2) * m1 * v1^2
The initial kinetic energy of the clay is given by: KE2 = (1/2) * m2 * v2^2
Since the clay sticks to the car, the final kinetic energy is given by: KEf = (1/2) * (m1 + m2) * vf^2
According to the principle of conservation of kinetic energy, we have KE1 + KE2 = KEf
Substituting the given values:
m1 = 2000 kg (mass of the car)
v1 = 2.0 m/s (initial velocity of the car)
m2 = 12 kg (mass of the clay)
v2 = (2012 kg • vf - 4000 kg•m/s) / 12 kg (initial velocity of the clay)
vf = ? (final velocity to solve)
(1/2) * 2000 kg * (2.0 m/s)^2 + (1/2) * 12 kg * [(2012 kg • vf - 4000 kg•m/s) / 12 kg]^2 = (1/2) * (2000 kg + 12 kg) * vf^2
Simplifying the equation further:
2000 kg • (2.0 m/s)^2 + [(2012 kg • vf - 4000 kg•m/s) / 12 kg]^2 = (2012 kg) / 2 • vf^2
Solve this equation to find the value of vf, which will be the final velocity of the car and clay after the collision.
After finding vf, substitute the value back into the equation for v2 = (2012 kg • vf - 4000 kg•m/s) / 12 kg to get the initial velocity of the clay (v2).
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Let's assume that the initial velocity of the car is u, and the final velocity of the car and clay together is v.
Before the collision, the momentum of the car is given by the formula:
P(car) = mass(car) × velocity(car)
P(car) = 2000 kg × 2.0 m/s
P(car) = 4000 kg·m/s
The momentum of the clay is given by the formula:
P(clay) = mass(clay) × velocity(clay)
P(clay) = 12 kg × velocity(clay)
According to the principle of conservation of momentum:
P(car) + P(clay) = P(car+clay)
4000 kg·m/s + 12 kg × velocity(clay) = (2000 kg + 12 kg) × v
Simplifying and solving for v:
4000 kg·m/s + 12 kg × velocity(clay) = 2012 kg × v
12 kg × velocity(clay) = 2012 kg × v - 4000 kg·m/s
velocity(clay) = (2012 kg × v - 4000 kg·m/s) / 12 kg
Now, let's plug in the given values:
velocity(clay) = (2012 kg × v - 4000 kg·m/s) / 12 kg
2 m/s = (2012 kg × v - 4000 kg·m/s) / 12 kg
Simplifying further:
24 kg·m/s = 2012 kg × v - 4000 kg·m/s
24 kg·m/s + 4000 kg·m/s = 2012 kg × v
(24 kg·m/s + 4000 kg·m/s) / 2012 kg = v
4024 kg·m/s / 2012 kg = v
v ≈ 2.00 m/s
Therefore, to stop the car, you should fire the clay with an approximate velocity of 2.00 m/s.