An internal explosion breaks an object into two fragments. One fragment is 2.35 kg moving 30 degrees north of east at 3.5 m/s and the other fragment is 2.65 kg. (a) What is the total mass of the object? (b) What is the velocity of the other fragment.
m = 2.35 + 2.65
initial momentum = final momentum = 0
There is no momentum perpendicular to the path of the first particle so
the second particle moves at 30 degrees South of West (straight back)
2.35 * 3.5 = 2.65 * |Vb|
|Vb| = (2.35/2.65) * 3.5
(a) Well, when it comes to explosions and fragments, it's always a messy situation. But let's see if we can make sense of it! If we're talking about two fragments, one weighing 2.35 kg and the other 2.65 kg, then the total mass of the object would be the sum of these two weights. So, the total mass would be 2.35 kg + 2.65 kg, which gives us... um... 5 kg!
(b) Now, when it comes to the velocity of the other fragment, we have some information about the first one. It's moving 30 degrees north of east at a speed of 3.5 m/s. But we don't know anything about the second fragment's velocity, so we can't really determine it from the given information. Maybe it got tired and decided to take a nap instead? Who knows!
To solve this problem, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the explosion should be equal to the total momentum after the explosion.
(a) To find the total mass of the object before the explosion, we need to add the masses of the two fragments. The total mass of the object is:
Total mass = mass of fragment 1 + mass of fragment 2
Total mass = 2.35 kg + 2.65 kg
Total mass = 5 kg.
Therefore, the total mass of the object is 5 kg.
(b) To find the velocity of the other fragment, we need to use the conservation of momentum equation. The equation is:
(mass of fragment 1 * velocity of fragment 1) + (mass of fragment 2 * velocity of fragment 2) = 0.
Let's assume the velocity of the other fragment is v2.
(2.35 kg * 3.5 m/s * cos(30°)) + (2.65 kg * v2) = 0
Simplifying the equation:
2.35 kg * 3.5 m/s * cos(30°) + 2.65 kg * v2 = 0
v2 = - (2.35 kg * 3.5 m/s * cos(30°)) / 2.65 kg.
Now, substituting the values:
v2 = - (2.35 kg * 3.5 m/s * cos(30°)) / 2.65 kg
v2 ≈ -1.93 m/s.
To solve this problem, we need to use the principles of conservation of momentum and conservation of kinetic energy.
(a) Total mass of the object:
The total mass of the object can be found by adding the individual masses of the two fragments. In this case, the mass of one fragment is given as 2.35 kg, and the mass of the other fragment is given as 2.65 kg. Adding these values together gives us:
Total mass = 2.35 kg + 2.65 kg
Total mass = 5 kg
So, the total mass of the object is 5 kg.
(b) Velocity of the other fragment:
To find the velocity of the other fragment, we can use the principle of conservation of momentum. According to this principle, the total momentum of an isolated system remains constant before and after the explosion.
The momentum (p) of an object is given by the product of its mass (m) and velocity (v):
p = m * v
Before the explosion, the object was one entity, so the initial momentum is zero. After the explosion, the two fragments move in different directions with different velocities. Let's denote the velocity of the other fragment as v2.
According to the conservation of momentum:
(initial momentum) = (final momentum)
0 = (mass of fragment 1 * velocity of fragment 1) + (mass of fragment 2 * velocity of fragment 2)
0 = (2.35 kg * 3.5 m/s) + (2.65 kg * velocity of fragment 2)
Now, we can solve this equation to find the velocity of the other fragment, v2. Rearranging the equation we have:
(2.35 kg * 3.5 m/s) = - (2.65 kg * velocity of fragment 2)
Solving for v2:
velocity of fragment 2 = -((2.35 kg * 3.5 m/s) / 2.65 kg)
velocity of fragment 2 ≈ -3.09 m/s
Therefore, the velocity of the other fragment is approximately -3.09 m/s. The negative sign indicates that it is moving in the opposite direction of the first fragment.