during a snowball fight two balls with masses of 0.28 and 0.75 kg, respectively , are thrown in such a manner that they meet head-on and combine to form a single mass. the magnitude of initial velocity for each is 15 m/s. what is the speed of the combined mass immediately after collision?
m1v1 + m2v2 = (m1+m2)vf
And watch your directions, one must be negative.
Well, let's calculate that snowball collision with a touch of humor, shall we? Picture this: two snowballs, each with their own unique personalities, hurtling towards each other in a dramatic clash of snowy destiny.
Now, the mass of one snowball is 0.28 kg, and the other snowball weighs in at 0.75 kg. Both of them have impressive initial velocities of 15 m/s. They meet head-on, ready to merge into a single, combined mass.
After the collision, with the precision of a circus acrobat, we need to determine the speed of this merged snowball mass. We can find the answer by applying the principle of conservation of momentum, which states that the total momentum before the collision should be equal to the total momentum after the collision.
The initial momentum is given by the sum of the individual momenta of the snowballs. Momentum (p) is calculated as the product of mass (m) and velocity (v): p = m * v.
For the first snowball, p1 = 0.28 kg * 15 m/s = 4.2 kg·m/s.
For the second snowball, p2 = 0.75 kg * 15 m/s = 11.25 kg·m/s.
Now, since the snowballs collide and stick together, their final total momentum will be the sum of their initial momenta: pf = p1 + p2 = 15.45 kg·m/s.
At this point, the combined mass of the snowballs will be the sum of their individual masses: m = 0.28 kg + 0.75 kg = 1.03 kg.
Finally, we can find the velocity of the combined mass by dividing the final momentum by the combined mass: vf = pf / m = 15.45 kg·m/s ÷ 1.03 kg.
*Drumroll, please*
And the velocity of the combined mass after the collision is approximately 15 m/s. Voilà! The snowballs have united with a speed that's as impressive as a squirrel on ice skates.
Hope that puts a grin on your face, just like seeing clowns in a snowball fight!
To find the speed of the combined mass immediately after the collision, we can use the principle of conservation of momentum.
The momentum of an object is given by the product of its mass and velocity (p = mv). According to the conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision.
Let's denote the initial velocity of both snowballs as v, and the final velocity of the combined mass as V (which we need to find).
Before the collision:
Initial momentum of the first snowball (m1v1) = (0.28 kg)(15 m/s) = 4.2 kg·m/s
Initial momentum of the second snowball (m2v2) = (0.75 kg)(15 m/s) = 11.25 kg·m/s
After the collision:
Final momentum of the combined mass (MV) = (m1 + m2)V
Now, we equate the initial momentum to the final momentum:
m1v1 + m2v2 = (m1 + m2)V
Substituting the given values:
(0.28 kg)(15 m/s) + (0.75 kg)(15 m/s) = (0.28 kg + 0.75 kg)V
Simplifying the equation:
4.2 kg·m/s + 11.25 kg·m/s = 1.03 kg·V
15.45 kg·m/s = 1.03 kg·V
To find V, divide both sides of the equation by 1.03 kg:
V = 15.45 kg·m/s / 1.03 kg
V ≈ 15 m/s
Therefore, the speed of the combined mass immediately after the collision is approximately 15 m/s.
To find the speed of the combined mass immediately after the collision, we can use the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision, provided no external forces act on the objects.
The momentum (p) of an object is given by the product of its mass (m) and velocity (v): p = m * v.
Let's calculate the initial momentum of the two snowballs before the collision:
For the 0.28 kg snowball:
Initial momentum = mass * velocity = 0.28 kg * 15 m/s
For the 0.75 kg snowball:
Initial momentum = mass * velocity = 0.75 kg * 15 m/s
Now, the total initial momentum of the system is the sum of the individual momenta:
Total initial momentum = (0.28 kg * 15 m/s) + (0.75 kg * 15 m/s)
Next, we need to use the principle of conservation of momentum to find the total momentum of the combined mass after the collision. Since the two snowballs meet head-on and combine to form a single mass, their velocities will have opposite signs.
The final mass of the combined snowballs is the sum of their masses:
Final mass = 0.28 kg + 0.75 kg
Now, we can calculate the final velocity of the combined mass using the formula for momentum:
Total initial momentum = Total final momentum
(mass1 * velocity1) + (mass2 * velocity2) = (combined mass * combined velocity)
(0.28 kg * 15 m/s) + (0.75 kg * -15 m/s) = (final mass * final velocity)
Solving this equation will give us the velocity of the combined mass. First, rearrange the equation:
(final mass * final velocity) = (0.28 kg * 15 m/s) + (0.75 kg * -15 m/s)
Now, substitute the final mass value:
(final velocity) = [(0.28 kg * 15 m/s) + (0.75 kg * -15 m/s)] / (0.28 kg + 0.75 kg)
Calculating this expression will give us the speed of the combined mass after the collision.