Answer the following questions with accept or reject, and explain why?   1) A force can be defined by the equation "w=mg". 2) If an object is thrown upward, it's potential energy will increase and the kinetic energy will decrease. 3) Regardless of the horizontal velocity, any object dropped vertically from the same height will hit the ground at the same time. 4) If I increase the mass of an object, it's inertia will also increase. 5) When the atomic number of an object is changed, the atomic mass will also change. 6) If I increase the amount of work done, I could also increase the amount of power (you may assume time remains constant).

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For number 1, the weight of an object is the gravitational force of attraction that the earth has for the body. That force is defined by W = mg.

For number 2, potential energy (PE) is given by the expression PE = mgh where h is the height of the body above a reference level (in this case the ground) and m and g have their usual meanings. So if the object is thrown upwards then its height h is increasing, thus its potential energy is also increasing. Kinetic energy on the other hand is given by the expression KE = (1/2)mv^2 where v is the velocity of the object. Because the object's velocity is upwards whilst gravity acts downwards, the object will slow down as it rises. So its kinetic energy will decrease. It gains potential energy and it loses an equal amount of kinetic energy.

With regards to number 3, gravity does not act horizontally - only vertically. So it falls with the same rate of acceleration regardless of the horizontal speed with which it is projected.

Inertia is a measure of the resistance of a body to changes in its motion when acted upon by an outside force. A heavier object will be more resistant to changes in its motion than a lighter one.

For number 5, the atomic number is the number of protons in the nucleus. So if you change the atomic number, you are changing the number of protons - the heaviest particle in the atom - and you are thus changing its mass. In fact, if you change the number of protons, you have a new atom for another element.

For the last question, Power = Work done/time. So if you do more work, you could increase your power, but only if you do it in the same time.

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1) Accept. According to Newton's second law of motion, force is defined as the product of mass (m) of an object and its acceleration (a). If an object is dropped from a height (on Earth), its acceleration can be given as acceleration due to gravity, g (that is, a = g). Then the force on the object (or its weight) will be given as F = W = mg.

2) Accept. When we throw an object upwards, its velocity reduces and it ultimately comes to a stop and then fall down, because of Earth's gravity. This clearly shows that as the object goes up, its kinetic energy (= `1/2 mv^2` ) reduces (as the velocity decreases) and ultimately becomes 0 (when velocity is 0, at the highest point in its trajectory). As the kinetic energy decreases, the object gains height and its potential energy (given as mgh, where h is the height of the object) increases. 

3) Accept. The horizontal and vertical motion can take place simultaneously, but are independent of each other. Think about it this way, if you are walking and the cellphone slips from your hand, it will fall down right next to your feet. Same will the scenario, if you were just standing and it fell down. In both case, your motion is independent of phone's vertical motion and it will take the same amount of time to fall down. In other words, the vertical motion is affected by Earth's gravity and that is what govern's it. According to equations of motion, `V = 1/2 g t^2`  , the acceleration due to gravity will determine the motion and hence vertical motion will always take the same time.

4) Accept. The more massive an object is, higher is its inertia. Inertia can be defined as the property of an object that enables it to resist a change in its state of motion. That is, inertia will help an object stay at rest or in continuous motion, until sufficient external force overcomes inertia and cause a change in object's state of motion. Think about it this way, we can move a chair or a bicycle, but how difficult it is move a house or a car. Would you rather move a cat or an elephant. Thus, more mass means more inertia.

5) Accept. The atomic number of an element is same as the number of protons. The atomic mass is the sum of number of protons and neutrons in an atom. When the atomic number changes, that is number of protons change; so does its atomic mass. The elements are arranged in the periodic table and each element corresponds to a different atomic number. When the atomic number changes, the element itself changes. For example, the object changes from carbon to nitrogen as one proton is added to it. And they each have a different atomic mass.

6) Accept. Power is defined as work done per unit time. If we increase the amount of work done (while keeping the time constant), the power will increase. Think about it this way, if you take 2 minutes to climb a set of stairs and then you do the same twice in 2 minute (while running up the stairs); your body would have done more work and hence, would have spent more power on the exercise.

Hope this helps.  

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