A 2.1-kg brick is placed gently upon a 2.9-kg cart originally moving with a speed of 26 cm/s.
Determine the post-collision speed of the combination of brick and cart.
To determine the post-collision speed of the combination of the brick and cart, we can apply the law of conservation of momentum.
The law of conservation of momentum states that the total momentum of an isolated system remains constant before and after a collision. Mathematically, it can be expressed as:
(m1 * v1) + (m2 * v2) = (m1 + m2) * vf
Where:
m1 and m2 are the masses of the objects involved in the collision,
v1 and v2 are the initial velocities of the objects, and
vf is the final velocity of the combined objects after the collision.
In this case, the brick and cart collide, and we want to find the final velocity of the combination.
Given:
m1 (mass of the brick) = 2.1 kg
m2 (mass of the cart) = 2.9 kg
v1 (initial velocity of the brick) = 0 cm/s (since it is placed gently)
v2 (initial velocity of the cart) = 26 cm/s
We need to convert the velocities from centimeters per second (cm/s) to meters per second (m/s) for consistency in the units. Since 1 m = 100 cm, we divide the velocities by 100.
v1 = 0 cm/s / 100 = 0 m/s
v2 = 26 cm/s / 100 = 0.26 m/s
Now let's substitute these values into the momentum equation:
(2.1 kg * 0 m/s) + (2.9 kg * 0.26 m/s) = (2.1 kg + 2.9 kg) * vf
0 + 0.754 kg m/s = 5 kg * vf
Rearranging the equation to solve for vf:
vf = (0 + 0.754 kg m/s) / 5 kg
vf = 0.1508 m/s
Therefore, the post-collision speed of the combination of the brick and cart is approximately 0.1508 m/s.