Two carts with masses of 15.5 kg and 1.0 kg, respectively, move in opposite directions on a frictionless horizontal track with speeds of 6.0 m/s and 2.0 m/s, respectively. The carts stick together after colliding head-on. Find the final speed of the two carts.

m/s

(15.5 x 6.0) + (1.0 x 2.0) = 92 kgm/s

92/16.5 = 5.58 m/s (2d.p)

To find the final speed of the two carts after colliding, we can use the principle of conservation of momentum.

The principle of conservation of momentum states that the total momentum of a system before a collision is equal to the total momentum of the system after the collision, provided that no external forces act on the system.

The momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v). Mathematically, it is represented as p = m * v.

Before the collision:
- Cart 1: mass = 15.5 kg, velocity = 6.0 m/s
- Cart 2: mass = 1.0 kg, velocity = -2.0 m/s (since it moves in the opposite direction, its velocity is considered negative)

We can calculate the initial momentum of each cart by multiplying its mass by its velocity:

Initial momentum of Cart 1 = 15.5 kg * 6.0 m/s = 93.0 kg·m/s
Initial momentum of Cart 2 = 1.0 kg * -2.0 m/s = -2.0 kg·m/s

The negative sign for Cart 2's momentum indicates that it is moving in the opposite direction.

Total initial momentum before the collision = 93.0 kg·m/s - 2.0 kg·m/s = 91.0 kg·m/s

After the collision, the carts stick together and move as one object. Let's assume their final velocity is v.

The mass of the combined system (the two carts stuck together) is the sum of their individual masses: 15.5 kg + 1.0 kg = 16.5 kg.

Using the principle of conservation of momentum, we equate the initial momentum to the final momentum:

Total initial momentum before the collision = Total final momentum after the collision

91.0 kg·m/s = 16.5 kg * v

To find v, we divide both sides of the equation by the combined mass of the carts:

v = 91.0 kg·m/s / 16.5 kg

Calculating this, we get:

v = 5.515 m/s

Therefore, the final speed of the two carts, after sticking together, is 5.515 m/s.

scsdc

the answer is 69

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