Three carts of masses 4kg, 10 kg, and 3 kg move on a frictionless horizontal surface with initial speeds of 5 m/s, 3 m/s, and 4 m/s. If the carts all stick together after the collisions, what will be the final velocity of the combined mass?
Help ASAP please. Step by step to get the answer
add the initial momnetums. Final momentum = (4+10+3)V solve for V
I still don't get it. Can you show me the equation with the numbers plugged into it please
Never mind I got it
To find the final velocity of the combined mass, 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.
1. Calculate the initial momentum (P_initial) of each cart:
- For the 4 kg cart: P_initial = mass_1 * velocity_1
P_initial1 = 4 kg * 5 m/s = 20 kg·m/s
- For the 10 kg cart: P_initial = mass_2 * velocity_2
P_initial2 = 10 kg * 3 m/s = 30 kg·m/s
- For the 3 kg cart: P_initial = mass_3 * velocity_3
P_initial3 = 3 kg * 4 m/s = 12 kg·m/s
2. Calculate the total initial momentum (P_initial_total):
P_initial_total = P_initial1 + P_initial2 + P_initial3
= 20 kg·m/s + 30 kg·m/s + 12 kg·m/s
= 62 kg·m/s
3. After the collision, the carts stick together, so we can calculate the total mass (m_total) of the combined carts:
m_total = mass_1 + mass_2 + mass_3
= 4 kg + 10 kg + 3 kg
= 17 kg
4. To find the final velocity (V_final) of the combined mass, we can use the formula for momentum:
P_final = m_total * V_final
5. Rearrange the formula to solve for V_final:
V_final = P_final / m_total
6. Substitute the calculated total initial momentum (P_initial_total) and total mass (m_total) into the formula:
V_final = 62 kg·m/s / 17 kg
7. Calculate the final velocity:
V_final ≈ 3.65 m/s
Therefore, the final velocity of the combined mass after the collision is approximately 3.65 m/s.