In a fireworks display a 3 kg body moving at 4 km/h due north explodes into three equal pieces: A, at 4 km/h east; B, at 5 km/h 37 degrees south of west; and C, at 15 km/h due north. After the explosion, what is the total momentum of all the pieces?
The same as before the explosion (First law)
12 due north
afsdfa
To find the total momentum of all the pieces after the explosion, we need to calculate the momentum of each individual piece and then add them together.
Momentum is calculated by multiplying the mass of an object by its velocity. The formula for momentum (p) is:
p = m * v
Where:
p = momentum
m = mass
v = velocity
Let's calculate the momentum of each piece separately.
For Piece A:
Mass (m) = 3 kg (given)
Velocity (v) = 4 km/h east
Before we calculate the momentum, we need to convert the velocity from km/h to m/s. To do this, we multiply the velocity by 1000/3600 (because 1 km/h = 1000 m/3600 s).
Converting the velocity to m/s:
4 km/h * (1000 m/3600 s) = 1.111 m/s (approximately)
Now, we can calculate the momentum of Piece A:
Momentum (pA) = m * v
pA = 3 kg * 1.111 m/s
pA = 3.333 kg m/s
For Piece B:
Mass (m) = 3 kg (given)
Velocity (v) = 5 km/h 37 degrees south of west
To calculate the momentum, we first need to determine the velocity components in the horizontal (west-east) and vertical (south-north) directions.
Using trigonometry, we can find the horizontal and vertical components of the velocity:
Horizontal component (v_horizontal) = v * cos(angle)
v_horizontal = 5 km/h * cos(37 degrees) = 3.974 km/h
Vertical component (v_vertical) = v * sin(angle)
v_vertical = 5 km/h * sin(37 degrees) = 3 km/h
Now, we need to convert these components to m/s. Following the same procedure as before:
Horizontal component (v_horizontal) = 3.974 km/h * (1000 m/3600 s) = 1.104 m/s (approximately)
Vertical component (v_vertical) = 3 km/h * (1000 m/3600 s) = 0.833 m/s (approximately)
Now, we can calculate the momentum of Piece B:
Momentum (pB) = m * v
pB = 3 kg * (1.104 m/s - 0.833 m/s)
pB = 0.81 kg m/s
For Piece C:
Mass (m) = 3 kg (given)
Velocity (v) = 15 km/h due north
Converting the velocity to m/s:
15 km/h * (1000 m/3600 s) = 4.167 m/s (approximately)
Now, we can calculate the momentum of Piece C:
Momentum (pC) = m * v
pC = 3 kg * 4.167 m/s
pC = 12.501 kg m/s (approximately)
Finally, to find the total momentum of all the pieces, we add up the individual momenta:
Total Momentum = pA + pB + pC
Total Momentum ≈ 3.333 kg m/s + 0.81 kg m/s + 12.501 kg m/s
Total Momentum ≈ 16.644 kg m/s
So, after the explosion, the total momentum of all the pieces is approximately 16.644 kg m/s.