Object 1 (mass=5.5 kg) traveling in the +x direction at a speed of 12.40m/s undergoes an inelastic collision with Object 2 (mass=4.80kg) which is at rest. Object two flies off at a speed of 7.80m/s and an angle θ2=32.4 °. It is possible that Object 1 travels back and to the left, though it is not possible for it to travel in the -y direction.
A)What is the total momentum in x direction after the collision?
B) What is the momentum of Object 1 in the y direction after the collision
C) What is the speed of Object 1 after the collision?
D) What is the angle θ1 in degrees?
To answer these questions, we first need to understand the principles of conservation of momentum and conservation of kinetic energy in a collision.
Conservation of momentum states that the total momentum of an isolated system before a collision is equal to the total momentum after the collision. Mathematically, this can be expressed as:
ΣP_initial = ΣP_final
Where ΣP_initial represents the initial momentum and ΣP_final represents the final momentum.
In an inelastic collision, the objects stick together and move as one after the collision. Therefore, the final momentum of the system is just the sum of the initial momenta of the individual objects.
Now let's apply these principles to answer the given questions:
A) What is the total momentum in the x direction after the collision?
Since Object 2 is initially at rest, its initial momentum in the x direction is zero.
The initial momentum of Object 1 is given by:
P_initial1 = m1 * v1_initial
P_initial1 = (5.5 kg) * (12.40 m/s)
So, the total initial momentum in the x direction is:
ΣP_initial_x = P_initial1
After the collision, the objects stick together, so they have the same final momentum in the x direction. Therefore, the total final momentum in the x direction is also:
ΣP_final_x = P_final = P_initial1
B) What is the momentum of Object 1 in the y direction after the collision?
In this collision, it is not possible for Object 1 to travel in the -y direction.
Therefore, the momentum of Object 1 in the y direction after the collision is zero.
C) What is the speed of Object 1 after the collision?
In an inelastic collision, the objects stick together and move with a common final velocity. Let's call this final velocity V_final.
Using the conservation of momentum in the x direction, we have:
ΣP_initial_x = ΣP_final_x
P_initial1 = (m1 + m2) * V_final
(5.5 kg) * (12.40 m/s) = (5.5 kg + 4.80 kg) * V_final
V_final = [(5.5 kg) * (12.40 m/s)] / (5.5 kg + 4.80 kg)
Once we have V_final, we can calculate the speed of Object 1 after the collision by finding the magnitude of this velocity vector:
Speed of Object 1 = |V_final| = √(V_final_x^2 + V_final_y^2)
Note: V_final_x represents the x component of V_final, and V_final_y represents the y component of V_final.
D) What is the angle θ1 in degrees?
To find the angle θ1, we can use trigonometry. Since we know the x and y components of V_final, we can use the following formulas:
θ1 = arctan(V_final_y / V_final_x)
The angle θ1 will give us the direction of the velocity vector of Object 1 after the collision.