Explanation:
An elastic band is hung on a hook and a mass is hung on the lower end of the band. When the mass is pulled downward and then released, it vibrates vertically. The equation of motion is given by :
Where
s is in centimeters
t is in seconds
Velocity of the particle,
Acceleration of the particle,
Hence, this is the required solution.
The velocity of the combined mass after the collision is 0.84 ms-1.
<u>Explanation:</u>
According to law of conservation of momentum, the change in momentum before collision will be equal to the change in momentum of the objects after collision in isolated system.
But as it is perfectly inelastic collision in the present case, the final momentum will be based on the product of total mass of both the object with the velocity with which the collision occurred. This form is attained from the law of conservation of momentum as shown below:
So as law of conservation of momentum,
Here = 3 kg and = 2 kg are the masses of objects 1 and 2, = 1.4 m/s and = 0 are the initial velocities of object 1 and object 2, and are the final velocities of the objects.
So after collision, object 1 get sticked to object 2 and move together with equal velocity = = . Thus the above equation will become,
So the final velocity is
Thus,
= 0.84 ms-1.
Answer:
Magnification, m = -0.42
Explanation:
It is given that,
Height of diamond ring, h = 1.5 cm
Object distance, u = -20 cm
Radius of curvature of concave mirror, R = 30 cm
Focal length of mirror, f = R/2 = -15 cm (focal length is negative for concave mirror)
Using mirror's formula :
, f = focal length of the mirror
v = -8.57 cm
The magnification of a mirror is given by,
m = -0.42
So, the magnification of the concave mirror is 0.42. Thew negative sign shows that the image is inverted.
<h2>Right answer: acceleration due to gravity is always the same </h2><h2 />
According to the experiments done and currently verified, in vacuum (this means there is not air or any fluid), all objects in free fall experience the same acceleration, which is <u>the acceleration of gravity</u>.
Now, in this case we are on Earth, so the gravity value is
Note the objects experience the acceleration of gravity regardless of their mass.
Nevertheless, on Earth we have air, hence <u>air resistance</u>, so the afirmation <em>"Free fall is a situation in which the only force acting upon an object is gravity" </em>is not completely true on Earth, unless the following condition is fulfiled:
If the air resistance is <u>too small</u> that we can approximate it to <u>zero</u> in the calculations, then in free fall the objects will accelerate downwards at and hit the ground at approximately the same time.
Answer:
Explanation:
<u>Instant Velocity and Acceleration
</u>
Give the position of an object as a function of time y(x), the instant velocity can be obtained by
Where y'(x) is the first derivative of y respect to time x. The instant acceleration is given by
We are given the function for y
Note we have changed the last term to be quadratic, so the question has more sense.
The velocity is
And the acceleration is