The Gravitational Force Experienced By An Object Is Its ____

[Astryd Boschee]

Momentumcan be thought of as mass in motion. An object has momentum if it has its mass in motion. It matters not whether the object is of large mass or small mass, moving with constant speed or accelerating; if the object is MOVING, then it has momentum!

Since being dropped from the same height, the balls will be moving with the same pre-collision velocity (assuming negligible air resistance). Upon collision with the ground, the velocity will have to be reduced to zero - that is, the ball will cease moving downwards. This decrease in velocity constitutes the first portion of the velocity change. If the ball bounces, then there is an additional velocity change sending the ball back upwards opposite the original direction. Thus, for the same collision time, bouncing involves a greater velocity change, a greater momentum change, and therefore a greater impulse.

In any collision, there are always four quantities which are the same for both objects involved in the collision. Each object experiences the same force (Newton's third law) for the same amount of time, leading to the same impulse, and subsequently the same momentum change. Only the acceleration and the velocity change can differ for the two colliding objects. The lower mass object always receives the greater velocity change and acceleration.

Rockets accelerate in outer space by means of Newton's third law of motion. It does not matter that there is no air outside of the rocket. Rockets produce their own gas by burning fuels. The combustion of rocket fuels produces gaseous products. The rocket's thrusters push these gases backwards (or rightwards, or leftwards, or ...) and the gases push the rocket forwards (or leftwards, or rightwards, or ...). Thus, rockets indeed can and do accelerate in outer space.

11. In order to catch a ball, a baseball player naturally moves his or her hand backward in the direction of the ball's motion once the ball contacts the hand. This habit causes the force of impact on the players hand to be reduced in size principally because ___.

Increasing the time over which the ball's momentum is brought to 0 will decrease the force required to stop it. Suppose a ball is coming at you with 100-units of momentum. An impulse of 100-units would be required to stop the ball. Regardless of how the impulse is accomplished (big F, little t or little F, big t), there must be 100-units of it. Imparting such an impulse over a long time results in a small force.

In any collision or explosion involving two objects, the momentum change for each object is the same. So both the bullet and the gun encounter the same momentum change. The momentum change is simply the mass multiplied by the velocity change. Thus, the velocity change would only be the same if their masses were the same. Otherwise, the smaller-mass object receives a greater velocity change.

In any collision, there are always four quantities which are the same for both objects involved in the collision. Each object experiences the same force (Newton's third law) for the same amount of time, leading to the same impulse, and subsequently the same momentum change. Only the acceleration and the velocity change can differ for the two objects. The object with the least mass always receives the greatest velocity change and acceleration.

If an object is at rest, then all the forces acting upon the object must be zero. The net force on any one of the boxes is 0 Newtons. Subsequently, in each case, the support force (which we have called the "normal force throughout this course) acting upwards on any of the boxes must be equal to the force of gravity on that box (i.e., the weight) plus the amount of load exerted from above (which would be equivalent to the weight of the other boxes located above the box). So for box Y, the support force acting upward would be equal to 9 N while the net force is still 0 Newtons. And for box Z, the support force is 19 N, sufficient to balance the 10-N gravitational force plus the 9-N of force resulting from the other two boxes bearing down on it.

The momentum of an object is calculated as the product of mass and velocity. Thus, the momentum is directly proportional to the mass of the object. If the mass of an object is somehow doubled, the momentum is doubled as well.

Please don't answer A (for it will make Newton roll over in his grave and he's getting quite tired of that). Perhaps you've heard that "for every action, there is an equal and opposite ...". Choice B is invalid; speed is not something that becomes concentrated or squeezed into an object. Choice D is invalid; ask anyone who's fired a rifle if the rifle is set into motion by the firing of the bullet. (Of course, since it is set in motion, its momentum is not unchanged.) Because of the large mass of the rifle, the acceleration and the recoil speed of the rifle is small.

21. Two objects, A and B, have the same size and shape. Object A is twice as massive as B. The objects are simultaneously dropped from a high window on a tall building. (Neglect the effect air resistance.) The objects will reach the ground at the same time but object A will have a greater ___. Choose all that apply.

The two objects free-fall at the same rate of acceleration, thus giving them the same speed when they hit the ground. The heavier object however has more momentum since momentum takes into account both the speed and the mass of the object (p=m*v).

Both A and C are correct. Padded dashboard serve to increase the time over which the momentum of a passenger is reduced to zero. With this increase in time, there is a decrease in force (big T, little f).

The impulse acting upon the passenger is not changed. The passenger still must have his/her mass slowed down from the pre-impact velocity to zero velocity. This means the velocity change is the same whether the collision occurs with a padded dashboard, an air bag or a glass windshield. Since the velocity change is independent of the collision time, the momentum change and the required impulse are also independent of the collision time.

24. A wad of chewed bubble gum is moving with 1 unit of momentum when it collides with a heavy box that is initially at rest. The gum sticks to the box and both are set in motion with a combined momentum that is ___.

Before the collision, the total system momentum is 1 unit - all due to the motion of the wad of gum. Since momentum must be conserved, the total momentum of the box and gum after the collision must also be 1 unit.

A large force acting upon a small mass will result in a large acceleration (a=F/m) and subsequently a large velocity change (Delta v = a*t). This rules out choices A and D. A large force and for a long time will result in a large impulse and therefore a large momentum change. This rules out choice C.

26. Consider the concepts of work and energy (presuming you have already studied it) and those of impuse and momentum. Force and time is related to momentum change in the same manner as force and displacement pertains to ___________.

A force multiplied by a time gives an impulse which will cause (and be equal to) a momentum change. In the same manner, a force multiplied by a displacement gives work which will cause (and be equal to) an energy change. Take the time to reread those two sentences because it relates two big concepts.

Don't make this harder than it is; the momentum change of an object can be found if the mass and the velocity change are known. In this equation, m=3 kg and the velocity change is -6 m/s. When finding the velocity change, always subtract the initial velocity from the final velocity (vf - vi).

There is a second means of determining the momentum change of an object (though it does not need to be used in this problem). The momentum change can also be found if the force and the time are known. Multiplying force*time yields the impulse and the impulse equals the momentum change.

The equation shows that force is directly related to the mass, directly related to the change in velocity, and inversely related to the time. So any change in mass will result in the same change in force; and any change in time will result in the inverse effect upon the force. In this case, doubling the mass (from M to 2M) will double the force and halving the time (from t to 1/2-t) will double the force. The combined effect of these two changes will make the new force four times bigger than the old force. This is a case of where equations can be a guide to thinking about how a change in one variable (or two variables) impacts other dependent variables.

The equation shows that force is directly related to the mass, directly related to the change in velocity, and inversely related to the time. So any change in mass will result in the same change in force; and any change in time will result in the inverse effect upon the force. In this case, doubling the mass (from M to 2M) will double the force and quartering the time (from t to 1/4-t) will quadruple the force. The combined effect of these two changes will make the new force eight times bigger than the old force. This is a case of where equations can be a guide to thinking about how a change in one variable (or two variables) impacts other dependent variables.

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