. What is the resultant momentum of a system of two particles with these masses and velocities: 3.75 kg moving north at 5.6 m/s and 4.2 kg moving northwest at 2.3 m/s?
on the NW movement, break it into N and W components.
Then add each direction, and recombine.
1231 m/s northwest
To find the resultant momentum of a system of two particles, we need to calculate the momentum of each particle and then add them together.
The momentum of an object is given by the equation:
Momentum = mass x velocity
Let's calculate the momentum of each particle:
Particle 1:
Mass = 3.75 kg
Velocity = 5.6 m/s
Momentum of Particle 1 = Mass x Velocity
= 3.75 kg x 5.6 m/s
= 21 kg·m/s (towards the north)
Particle 2:
Mass = 4.2 kg
Velocity = 2.3 m/s
To find the momentum of Particle 2, we need to break its velocity into its north and west components.
Given that it is moving northwest, we can use trigonometry to find the north and west components of its velocity.
The northwest direction can be represented as a 45-degree angle between north and west.
North Component of Velocity = Velocity x cos(angle)
= 2.3 m/s x cos(45°)
= 2.3 m/s x (√2 / 2)
= 1.62 m/s
West Component of Velocity = Velocity x sin(angle)
= 2.3 m/s x sin(45°)
= 2.3 m/s x (√2 / 2)
= 1.62 m/s
Now we have the north and west components of Particle 2's velocity.
Momentum of Particle 2 = Mass x Velocity
= 4.2 kg x 1.62 m/s (north component)
= 6.804 kg·m/s (north component)
Since the north component is the same as the velocity of Particle 1, we can add the momenta together.
Resultant Momentum = Momentum of Particle 1 + Momentum of Particle 2
= 21 kg·m/s (north) + 6.804 kg·m/s (north)
= 27.804 kg·m/s (north)
Therefore, the resultant momentum of the system of two particles is 27.804 kg·m/s towards the north.
To find the resultant momentum of a system of two particles, we first need to calculate the individual momenta of each particle. The momentum of an object is calculated by multiplying its mass with its velocity.
For the first particle:
Mass = 3.75 kg
Velocity = 5.6 m/s
Momentum = Mass * Velocity
Momentum1 = 3.75 kg * 5.6 m/s
Next, for the second particle:
Mass = 4.2 kg
Velocity = 2.3 m/s
Momentum = Mass * Velocity
Momentum2 = 4.2 kg * 2.3 m/s
Now, we find the x and y components of the momentum for each particle.
The first particle is moving directly north, so its y-component momentum is the same as its overall momentum.
Momentum1_y = 3.75 kg * 5.6 m/s (North) = 20.85 kg·m/s (North)
The second particle is moving northwest, which means it has both x and y components of momentum. To find these components, we need to split the velocity into its x and y components.
The velocity vector with a magnitude of 2.3 m/s can be split into its x and y components using trigonometry. Since the particle is moving northwest, the angle between the vector and the positive x-axis is 45 degrees.
Velocity2_x = velocity2 * cos(angle) = 2.3 m/s * cos(45°)
Velocity2_y = velocity2 * sin(angle) = 2.3 m/s * sin(45°)
Now we can find the x and y components of the momentum. Since the mass doesn't change, we multiply the mass with the corresponding velocity component to get the momentum component.
Momentum2_x = 4.2 kg * velocity2_x = 4.2 kg * (2.3 m/s * cos(45°))
Momentum2_y = 4.2 kg * velocity2_y = 4.2 kg * (2.3 m/s * sin(45°))
Next, we can add the x-components and y-components of the momentum separately to find the resultant momentum.
To add the x-components, we simply sum them up:
ResultantMomentum_x = Momentum2_x
To add the y-components, we also sum them up:
ResultantMomentum_y = Momentum1_y + Momentum2_y
Finally, to find the resultant momentum, we use the Pythagorean theorem:
ResultantMomentum = sqrt(ResultantMomentum_x^2 + ResultantMomentum_y^2)
Simply plug-in the respective values and calculate the result to get the resultant momentum of the system of two particles.