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  1. There was said to work when a force is applied onto an object along with the movements of the applied force. But for work, however to be done then three conditions apply: 1. Applied Force: One must apply forces on the affected object. 2. Displacement by the Applied force: The resultant movement of aRead more

    There was said to work when a force is applied onto an object along with the movements of the applied force. But for work, however to be done then three conditions apply:

    1. Applied Force: One must apply forces on the affected object.
    2. Displacement by the Applied force: The resultant movement of applying the force with the object having moved from position.
    3. Direction Alignment: The displacement must have a component in the direction of the applied force.

    Examples of Work:
    1. Lifting an Object: When you lift a book from the ground, you apply an upward force, and the book moves upwards. Here, work is done because the force and displacement are in the same direction.

    2. Pushing a cart: While the person applies the force for pushing the shopping cart, work gets done due to the displacement in the direction of the force.
    3. Pulling a Sled: One example of using force to do work would be pulling the sled on snowy surfaces. Applying force to push it in the direction of pull means work done is achieved.

    4. Lifting Water Using a Bucket: If a bucket is used to draw water from a well, then work is done as the bucket goes upwards because of the applied force.

    Work is not done when the object is stationary or the applied force is perpendicular to the displacement. This means holding an immovable object or carrying a load horizontally in which no vertical displacement is created does not include work.

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  2. When two bodies of masses m and 4m have the same amount of kinetic energy, their momenta differ because the relationship between kinetic energy and momentum is such that kinetic energy depends on both mass and the square of velocity, while momentum depends linearly on mass and velocity. The velocityRead more

    When two bodies of masses m and 4m have the same amount of kinetic energy, their momenta differ because the relationship between kinetic energy and momentum is such that kinetic energy depends on both mass and the square of velocity, while momentum depends linearly on mass and velocity.

    The velocity of a heavier body will have to be lower than that of a lighter body in order to have the same kinetic energy. For the kinetic energy being constant, the momentum of a body varies directly as the square root of its mass. So when their momenta are compared, the ratio of the momenta is equal to the square root of the ratio of the masses.

    In this case, the first body has mass m, while the second has a mass of 4m. The square root of their mass ratio, √1} : √4, gives the momentum ratio as 1:2. This means the body with four times the mass has double the momentum of the lighter body under equal kinetic energy conditions.

    Hence, the kinetic energy of both bodies is the same, but their momentum differs because of the mass in these bodies. It is greater in the former body compared with the later.

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  3. When a body breaks into two equal parts and is moving at some velocity, then its behavior may be analyzed using the principle of conservation of momentum. First, the whole body has some momentum because of the mass and the velocity of that body. The part, while breaking, travels backward with the saRead more

    When a body breaks into two equal parts and is moving at some velocity, then its behavior may be analyzed using the principle of conservation of momentum. First, the whole body has some momentum because of the mass and the velocity of that body. The part, while breaking, travels backward with the same speed of the original velocity of the body.

    In this case, if one part traces its trajectory with the same speed, we must calculate the velocity of the second part. Since momentum is conserved everywhere, the total momentum before and after the break will be the same.

    In that case, one part moving in the opposite direction with the same speed gives a negative contribution to the total momentum of the system. The other portion must make up for this alteration in order to ensure that the sum of the momentums remains unchanged. By the law of conservation of momentum, it is apparent that the second portion has to move in the forward direction at a greater velocity. More precisely, its velocity will be three times the original velocity of the body before it broke up. This shows how motion and the conservation principles are interrelated in physics. Finally, the second part of the body moves with a velocity three times greater than that of the original body.

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  4. We first need to understand the system. When the pendulum is at point P, it has maximum potential energy and no kinetic energy because it is momentarily at rest. Now, as the pendulum swings down to point Q, the potential energy gets converted into kinetic energy. To find the velocity of the pendulumRead more

    We first need to understand the system. When the pendulum is at point P, it has maximum potential energy and no kinetic energy because it is momentarily at rest. Now, as the pendulum swings down to point Q, the potential energy gets converted into kinetic energy. To find the velocity of the pendulum bob at point Q after losing 10% of its energy due to air resistance, we begin with understanding the system.

    However, during this process, the pendulum loses 10% of its total mechanical energy to air resistance. Thus, only 90% of the initial total energy is available for conversion into kinetic energy at point Q. The energy conversion results in the pendulum bob gaining speed as it moves downward.

    We can calculate the velocity at point Q. The lost energy is the one that reduces the kinetic energy the bob can have at the lowest point. The remaining energy translates into kinetic energy, which can be expressed in terms of the mass of the bob and its velocity.

    Ultimately, taking into consideration the energy transformations and the energy loss effect we observe that the pendulum bob at point Q will have a velocity of 6 meters per second. The answer is, therefore, 6 m/s.

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