Body A of mass 3.25 kg is moving in the +x-direction with a speed of 14.6 m/s. Body B of mass 4.33 kg is moving in the -y-direction with a speed of 7.84 m/s. What is the x-component of the velocity of the CM of the two bodies?
Question
Body A of mass 3.25 kg is moving in the +x-direction with a speed of 14.6 m/s. Body B of mass 4.33 kg is moving in the -y-direction with a speed of 7.84 m/s. What is the x-component of the velocity of the CM of the two bodies?
Solution
The x-component of the velocity of the center of mass (CM) can be calculated using the formula:
Vcm_x = (m1v1_x + m2v2_x) / (m1 + m2)
where:
- m1 and m2 are the masses of the two bodies,
- v1_x and v2_x are the x-components of the velocities of the two bodies.
Given that Body A is moving in the +x-direction, its velocity v1_x = 14.6 m/s. Since Body B is moving in the -y-direction, its x-component of velocity v2_x = 0 (as it has no motion in the x-direction).
So, substituting the given values into the formula, we get:
Vcm_x = ((3.25 kg * 14.6 m/s) + (4.33 kg * 0)) / (3.25 kg + 4.33 kg) = (47.45 kg*m/s) / 7.58 kg = 6.26 m/s
Therefore, the x-component of the velocity of the center of mass of the two bodies is 6.26 m/s.
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