a golf ball of mass 0.045 kg is moving in the +x direction with a speed of 9.0 m/s, and a baseball of mass 0.145 kg is moving in the -y direction with a speed of 7.0 m/s. What are the magnitude and direction if the total momentum of the system consisting of the two balls?
It is the resultant of the two perpendicular momentum vectors.
a golf ball of mass 0.045kg is moving in the +x-direction with a speed of 9.0m/s, and a baseball of mass 0.145kg is moving in the -y-direction with a speed of 7.0m/s. What are the magnitude and direction of the momentum of the system consisting of the two balls.
To find the magnitude and direction of the total momentum of the system consisting of the two balls, we first need to find the momentum of each ball and then add them together.
Momentum is defined as the product of an object's mass and its velocity. The formula for momentum is:
Momentum (p) = mass (m) × velocity (v)
Given information:
- Golf ball mass (m1) = 0.045 kg
- Golf ball velocity (v1) = 9.0 m/s in the +x direction
- Baseball mass (m2) = 0.145 kg
- Baseball velocity (v2) = 7.0 m/s in the -y direction
To find the momentum of each ball, we simply multiply the mass of each ball by its respective velocity:
Momentum of the golf ball (p1) = m1 × v1
Momentum of the golf ball (p1) = 0.045 kg × 9.0 m/s
Momentum of the baseball (p2) = m2 × v2
Momentum of the baseball (p2) = 0.145 kg × 7.0 m/s
Now we can calculate the total momentum by adding the individual momenta together:
Total momentum of the system (P) = p1 + p2
To find the magnitude of the total momentum, we take the absolute value:
Magnitude = |P|
To find the direction of the total momentum, we need to consider the signs of the individual momenta. Since the golf ball is moving in the +x direction and the baseball is moving in the -y direction, the total momentum will have both x and y components. We can find the direction by using trigonometry.
Direction = tan^(-1)(Py / Px)
where Py is the y component of the total momentum and Px is the x component of the total momentum.
Let's calculate the values:
Momentum of the golf ball (p1) = 0.045 kg × 9.0 m/s = 0.405 kg·m/s
Momentum of the baseball (p2) = 0.145 kg × 7.0 m/s = 1.015 kg·m/s
Total momentum of the system (P) = p1 + p2 = 0.405 kg·m/s + 1.015 kg·m/s = 1.42 kg·m/s
To calculate the magnitude:
Magnitude = |P| = |1.42 kg·m/s| = 1.42 kg·m/s
To calculate the direction:
Direction = tan^(-1)(Py / Px)
In this case, Py is the negative value of the momentum of the baseball since it is moving in the -y direction, and Px is the positive value of the momentum of the golf ball since it is moving in the +x direction.
Direction = tan^(-1)(-1.015 kg·m/s / 0.405 kg·m/s) = tan^(-1)(-2.506)
Using a calculator or trigonometric table, the direction is approximately -68.8 degrees.
Therefore, the magnitude of the total momentum of the system is 1.42 kg·m/s, and the direction is approximately -68.8 degrees relative to the positive x-axis.