Instantaenous velocity/center of mass? help

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In summary, a 10 kg wedge on a frictionless surface has a 5.0 kg block sliding down its rough inclined surface. At one instant, the block's velocity has a vertical component of 3.0 m/s and a horizontal component of 6.0 m/s. The question is asking for the velocity of the wedge at that instant. To solve this, we need to use the equation of motion for the center of mass of a system. The block's motion will cause the wedge to move, so we need to consider the system as a whole.
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dorkymichelle
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Homework Statement



A large wedge with a mass of 10 kg rests on a horizontal frictionless surface, as shown. A block with a mass of 5.0 kg starts from rest and slides down the inclined surface of the wedge, which is rough. At one instant the vertical component of the block's velocity is of 3.0 m/s and the horizontal component is 6.0 m/s. At that instant the velocity of the wedge is:

Homework Equations



The Attempt at a Solution


I'm not really sure where to get started... I think it has something to do with the center of mass but not sure what. Also, I'm confused as to how the block can cause the wedge to move. Can someone help me get started?
 
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What is the equation of motion for the center of mass of a system? Start there.
 

1. What is the definition of instantaneous velocity?

Instantaneous velocity is the rate of change of an object's position at a specific moment in time. It is a vector quantity that includes both magnitude and direction.

2. How is instantaneous velocity different from average velocity?

Instantaneous velocity is the velocity at a specific instant, while average velocity is the total displacement over a specific time interval. Instantaneous velocity is more precise and can capture changes in velocity over time, while average velocity gives an overall picture of an object's motion.

3. How do you calculate instantaneous velocity?

Instantaneous velocity can be calculated by finding the object's displacement at a specific moment and dividing it by the time interval. This can also be represented as the derivative of the object's position with respect to time.

4. What is the importance of center of mass in physics?

The center of mass is a crucial concept in physics as it helps determine the overall motion of an object. It is the point at which the mass of an object is evenly distributed in all directions, and it follows the laws of conservation of momentum and energy.

5. How is center of mass different from center of gravity?

While they are often used interchangeably, the center of mass and center of gravity are not the same. The center of mass is the point where the mass is evenly distributed, while the center of gravity is the point where the force of gravity acts on an object. In a uniform gravitational field, the center of mass and center of gravity will be in the same location.

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