Answer:
Free-fall is defined as the movement where the only force acting on an object is the gravitational force.
By the second Newton's law, we have that:
F = m*a
Where F = Force, m = mass, a = acceleration.
We can write this as:
a = F/m
And the gravitational force can be written as:
F = (G*M/r^2)*m
Where G is the gravitational constant, M is the mass of the Earth in this case, and r is the distance between both objects (the center of the Earth and the free-falling object)
As the radius of the Earth is really big, the term inside the parentheses is almost constant in the region of interest, then we can write:
G*M/r^2 ≈ g
And the gravitational force is:
F = g*m
And by the second Newton's law we had:
a = F/m = (g*m)/m = g
a = g
Then the acceleration does not depend on the mass of the object.
Then the thing that is common among the free-falling objects is the vertical acceleration.
Answer:
It has no effect on the amplitude.
Explanation:
When the sandbag is dropped, then the cart is at its maximum speed. Dropping the sand bag does not affect the speed instantly, this is because the energy remains within the system after the bag as been dropped. The cart will always return to its equilibrium point with the same amount of kinetic energy, as a result the same maximum speed is maintained.
Your question is missing one part as "magnification"
i have completed the missing part below
Answer:
a. 
b. 
Explanation:
For this type of numerical we will use the following formulas
......... Eq1
where,

refractive index of the medium surrounding refracting surface/object
i.e.
=

refractive index of the refracting surface/object
i.e. 
distance of object from the vertex of the refracting surface
distance of image from the vertex of the refracting surface
radius of curvature of the refracting surface
........... Eq2
where,
magnification
Convention:

Given:
=






because refraction surface is concave
Required:
a. 

b. 
Solution:
a. putting values in eq1, we get



cm
b. 
Answer:
d = 2.54 [m]
Explanation:
Through the theorem of work and energy conservation, we can find the work that is done. Considering that the energy in the initial state is only kinetic energy, while the energy in the final state is also kinetic, however, this is zero since the body stops.

where:
W = work [J]
Ek1 = kinetic energy at initial state [J]
Ek2 = kinetic energy at the final state = 0.
We must remember that kinetic energy can be calculated by means of the following expression.
![\frac{1}{2} *m*v^{2}-W=0\\W= \frac{1}{2} *4*(5)^{2}\\W= 50 [J]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%2Am%2Av%5E%7B2%7D-W%3D0%5C%5CW%3D%20%5Cfrac%7B1%7D%7B2%7D%20%2A4%2A%285%29%5E%7B2%7D%5C%5CW%3D%2050%20%5BJ%5D)
We know that work is defined as the product of force by distance.

where:
F = force [N]
d = distance [m]
But the friction force is equal to the product of the normal force (body weight) by the coefficient of friction.
![f=m*g*0.5\\f = 4*9.81*0.5\\f = 19.62 [N]](https://tex.z-dn.net/?f=f%3Dm%2Ag%2A0.5%5C%5Cf%20%3D%204%2A9.81%2A0.5%5C%5Cf%20%3D%2019.62%20%5BN%5D)
Now solving the equation for the work.
![d=W/F\\d = 50/19.62\\d = 2.54[m]](https://tex.z-dn.net/?f=d%3DW%2FF%5C%5Cd%20%3D%2050%2F19.62%5C%5Cd%20%3D%202.54%5Bm%5D)
frictional force that air exerts against a moving object