a 2kg car moving towards the right at 4 m/s collides head on with a 8 kg car moving towards the left at 2 m/s and they stick together. After the collision, the velocity of the combined boides is
Total momentum
= 2kg*4m/s + 8kg*(-2m/s)
= -8 kg-m/s
Final velocity for an inelastic collision
= -8 kg-m/s / (2kg+8kg)
= -0.8 m/s
Since the velocity is negative, the final velocity is towards the left.
Moving At 20m/s,a car with a mass of 7.0x10^2kg collides with a stationary truck with a mass of 1.4x10^3 kg. If the two vehicles stick together resulting from the collision, what is the velocity of the combined car and truck?
If a 10g bullet is fired from a 2000g rifle with a velocity of 500m/s at what velocity does the rifle recoil against the shooters shoulder??
Total momentum
= 2kg*4m/s + 8kg*(-2m/s)
= -8 kg-m/s
Final velocity for an inelastic collision
= -8 kg-m/s / (2kg+8kg)
= -0.8 m/s
Since the velocity is negative, the final velocity is towards the left.
However, you must state where the positive direction is, which in this it is upwards.
To find the velocity of the combined bodies after the collision, we can use the principle of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is the product of its mass and velocity. Mathematically, momentum (p) is given by the equation:
p = m * v
Given that the mass of the first car (m1) is 2 kg, the initial velocity of the first car (v1) is 4 m/s, the mass of the second car (m2) is 8 kg, and the initial velocity of the second car (v2) is -2 m/s (negative because it's moving in the opposite direction), we can calculate the initial momentum (p_initial) before the collision.
p_initial = (m1 * v1) + (m2 * v2)
Substituting the given values:
p_initial = (2 kg * 4 m/s) + (8 kg * -2 m/s)
= (8 kg*m/s) + (-16 kg*m/s)
= -8 kg*m/s
Since momentum is conserved in the collision, the total momentum after the collision will also be -8 kg*m/s.
After the collision, the two cars stick together and move as one combined body. Let's say the final mass of the combined bodies is M, and the final velocity is V. Therefore, we can write the equation for the momentum after the collision (p_final).
p_final = (M * V)
Since the total momentum after the collision is -8 kg*m/s, we can equate these values.
-8 kg*m/s = M * V
We have one equation with two unknowns, M and V. However, we can also use the principle of conservation of kinetic energy to solve for the final velocity. The kinetic energy before the collision is equal to the kinetic energy after the collision.
The kinetic energy (K) of an object is given by the equation:
K = (1/2) * m * v^2
Therefore, the initial kinetic energy (K_initial) is:
K_initial = (1/2) * (m1 * v1^2) + (1/2) * (m2 * v2^2)
Substituting the given values:
K_initial = (1/2) * (2 kg * (4 m/s)^2) + (1/2) * (8 kg * (-2 m/s)^2)
= (1/2) * (2 kg * 16 m^2/s^2) + (1/2) * (8 kg * 4 m^2/s^2)
= (1/2) * (32 kg * m^2/s^2) + (1/2) * (32 kg * m^2/s^2)
= 16 kg * m^2/s^2
Since kinetic energy is conserved in the collision, the total kinetic energy after the collision will also be 16 kg*m^2/s^2.
The kinetic energy (K_final) after the collision is:
K_final = (1/2) * (M * V^2)
Since the total kinetic energy after the collision is 16 kg*m^2/s^2, we can equate these values.
16 kg*m^2/s^2 = (1/2) * (M * V^2)
Now we have two equations and two unknowns, which we can solve simultaneously to find the final mass (M) and velocity (V) of the combined bodies.
It is important to note that we assumed the collision to be an elastic collision, where no external forces (like friction) are involved and kinetic energy is conserved.