Question

Two carts with masses of 4.2 kg and 3.2 kg move toward each other on a frictionless track with speeds of 5.4 m/s and 4.5 m/s, respectively. The carts stick together after colliding head-on. Find their final speed. Answer in units of m/s.

Answer 1

To calculate the final speed of two carts after a head-on collision where they stick together, we apply the conservation of momentum and solve the resultant equation accounting for direction.

Step-by-step explanation:

The question asks to find the final speed of two carts after they collide head-on and stick together on a frictionless track. We begin by using the principle of conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after the collision, assuming no external forces act on the system. The total momentum before the collision can be calculated by summing the products of mass and velocity for each cart, considering direction where one velocity is positive and the other is negative as the carts move toward each other. After they collide and stick together, the combined mass moves with a common velocity. As such, the equation to calculate the final speed after the collision becomes:

(4.2 kg * 5.4 m/s) + (3.2 kg * (-4.5 m/s)) = (4.2 kg + 3.2 kg) * v_final

By solving this equation, we can find the final speed v_final. The negative sign for one of the velocities indicates that the two carts are moving in opposite directions towards each other initially.

Performing the calculation yields the final answer.

Answer 2

Answer:the final speed is 5.01 m/s

Step-by-step explanation:

Momentum is the product of mass and velocity.

Cart 1 has a mass of 4.2kg and a speed 5.4 m/s

Cart 2 has a mass of 3.2kg and a speed 4.5 m/s

Total momentum before collision is

m1u1 + m2u2. It becomes

4.2×5.4 + 3.2×4.5 = 22.68 + 14.4

= 37.08kgm/s

The carts stick together after colliding head-on. This means that they move with a common velocity, v. Therefore, Total momentum after collision is (m1 + m2)v. It becomes

(4.2 + 3.2)v = 7.4v

According the the law of conservation of momentum, the total momentum before collision = the total momentum after collision. Therefore,

7.4v = 37.08

v = 37.08/7.4 = 5.01 m/s