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a 1000 kg automobile is moving along a straight highway at 10 m/s another car with mass 2000 kg and speed 20 m/s is 30m ahead of the first . the position of the center of mass of the system from first is
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a 1000 kg automobile is moving along a straight highway at 10 m/s ano...
Introduction:
In this scenario, we have two cars moving along a straight highway. The first car has a mass of 1000 kg and a speed of 10 m/s, while the second car has a mass of 2000 kg and a speed of 20 m/s. The second car is 30 meters ahead of the first car. We need to determine the position of the center of mass of the system from the first car.
Explanation:
To find the position of the center of mass of the system, we need to consider the masses and positions of both cars. The center of mass is a point that represents the average position of the entire mass distribution of a system.
Step 1: Calculate the center of mass of each car:
The center of mass of each car can be calculated using the formula:
x_cm = (m1 * x1 + m2 * x2) / (m1 + m2)
Where:
- x_cm is the position of the center of mass of the system.
- m1 and m2 are the masses of the first and second cars, respectively.
- x1 and x2 are the positions of the first and second cars, respectively.
For the first car:
- Mass (m1) = 1000 kg
- Position (x1) = 0 m (since it is the reference point)
For the second car:
- Mass (m2) = 2000 kg
- Position (x2) = 30 m (as given in the scenario)
Substituting the values into the formula, we get:
x_cm = (1000 kg * 0 m + 2000 kg * 30 m) / (1000 kg + 2000 kg)
Simplifying the equation:
x_cm = (60000 kg*m) / 3000 kg
x_cm = 20 m
Step 2: Interpretation:
The position of the center of mass of the system from the first car is 20 meters. This means that if we consider the system of both cars as a single object, the average position of its mass distribution is 20 meters from the first car.
In this scenario, we have two cars moving along a straight highway. The first car has a mass of 1000 kg and a speed of 10 m/s, while the second car has a mass of 2000 kg and a speed of 20 m/s. The second car is 30 meters ahead of the first car. We need to determine the position of the center of mass of the system from the first car.
Explanation:
To find the position of the center of mass of the system, we need to consider the masses and positions of both cars. The center of mass is a point that represents the average position of the entire mass distribution of a system.
Step 1: Calculate the center of mass of each car:
The center of mass of each car can be calculated using the formula:
Where:
- x_cm is the position of the center of mass of the system.
- m1 and m2 are the masses of the first and second cars, respectively.
- x1 and x2 are the positions of the first and second cars, respectively.
For the first car:
- Mass (m1) = 1000 kg
- Position (x1) = 0 m (since it is the reference point)
For the second car:
- Mass (m2) = 2000 kg
- Position (x2) = 30 m (as given in the scenario)
Substituting the values into the formula, we get:
Simplifying the equation:
Step 2: Interpretation:
The position of the center of mass of the system from the first car is 20 meters. This means that if we consider the system of both cars as a single object, the average position of its mass distribution is 20 meters from the first car.
Community Answer
a 1000 kg automobile is moving along a straight highway at 10 m/s ano...
20m( at t=0s.)
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a 1000 kg automobile is moving along a straight highway at 10 m/s another car with mass 2000 kg and speed 20 m/s is 30m ahead of the first . the position of the center of mass of the system from first is
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