Apply the general results obtained in the full analysis of motion under the influence of a constant force in Section 2.5 to answer the following questions. You hold a small metal ball of mass m a height h above the floor. You let go, and the ball falls to the floor. Choose the origin of the coordinate system to be on the floor where the ball hits, with y up as usual. Just after release, what are yi and vyi? Just before hitting the floor, what is yf? How much time ∆t does it take for the ball to fall? What is vfy just before hitting the floor? Express all results in terms of m, g, and h. How would your results change if the ball had twice the mass?
The initial location of the ball is
The initial speed of the ball is
The time the ball will need to fall is
The final speed of the ball is
The result won’t change when the mass of the ball will be twice the mass.
The time taken by ball to fall is given by,
The following is an explanation of conservation of momentum. There is a perfect match between total momentum of two particles before and after a collision occurs inside an isolated system between particle 1 and particle 2.
The principle of momentum is given by,
The force acting on the ball is purely gravitational force, here we assume that the speed of the ball is negligible, the net force on the ball can be given by,
Here, the initial location of the ball is
The initial speed of the ball is
The final location of ball before it hits the ground is
The time needed by ball to fall can be evaluated position equation,
Substitute the values in equation (1),
Thus, the time taken by the ball to fall is .
The final velocity of the ball can be evaluated using equation (1),
If the ball has twice the mass the result won’t change as it does not depend on the mass.
Thus, there is no change in result of the ball.
A ball is kicked on Earth from a location (on the ground) with initial velocity role="math" localid="1656668041027" . Neglecting air resistance: (a) What is the velocity of the ball 0.6 s after being kicked? (b) What is the location of the ball 0.6 s after being kicked? (c) What is the maximum height reached by the ball?
If the magnitude of the electric field in air exceeds roughly , the air break down and a spark forms. For a two-disk capacitor of radius 51 cm with a gap of 2 mm, if the electric field inside is just high enough that a spark occurs, what is the strength of the fringe field just outside the center of the capacitor?
Because the change of the momentum is equal to the net impulse, the relationship of momentum itself to the net force is somewhat indirect, as can be seen in this question. An object is initially moving in the + x direction with a magnitude of momentum p , with a net force of magnitude F acting on the object in either the + x or - x direction. After a very short time, say whether the magnitude of the momentum increases, decreases, or stays the same in each of the following situations:
a) the net force acts in the + x direction and F is constant.
b) the net force acts in the + x direction and F is increasing.
c) the net force acts in the + x direction and F is decreasing.
d) the net force acts in the - x direction and F is constant.
e) the net force acts in the - x direction and F is increasing.
f) the net force acts in the - x direction and F is decreasing.
You hang a 10 kg mass from a copper wire, and the wire stretches by .
(a) If you suspend the same mass from two copper wires, identical to the original wire, what happens?
(b) If you suspend the same mass from a copper wire with half the cross-sectional area but the same length as the original wire, what happens?
(c) If you suspend the same mass from a copper wire with the same cross-sectional area but twice the length of the original wire, what happens?
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