Answer:
E = 0.01 J
Explanation:
Given that,
The mass of the cart, m = 0.15 kg
The force constant of the spring, k = 3.58 N/m
The amplitude of the oscillations, A = 7.5 cm = 0.075 m
We need to find the total mechanical energy of the system. It can be given by the formula as follows :

Put all the values,

So, the value of total mechanical energy is equal to 0.01 J.
Answer:
h = 2.64 meters
Explanation:
It is given that,
Mass of one ball, 
Speed of the first ball,
(upward)
Mass of the other ball, 
Speed of the other ball,
(downward)
We know that in an inelastic collision, after the collision, both objects move with one common speed. Let it is given by V. Using the conservation of momentum to find it as :


V = 7.2 m/s
Let h is the height reached by the combined balls of putty rise above the collision point. Using the conservation of energy as :



h = 2.64 meters
So, the height reached by the combined mass is 2.64 meters. Hence, this is the required solution.
Answer:
diameter = 21.81 ft
Explanation:
The gravitational force equation is:

Where:
- F => Gravitational force or force of attraction between two masses
- M => Mass of asteroid 1
- m => Mass of asteroid 2
- R => Distance between asteroids 1 and 2 (from center of gravity)
We also know that the asteroids are identical so their masses are identical:
Since R is the distance between centers of the two asteroids and their diameters are identical (see attachment), we can conclude that:
We don´t know the mass of the asteroids but we know they are composed of pure iron, so we can relate their masses to their density:
This is going to be helpful because the volume of a sphere is:
And know we can write our original force of gravity equation in terms of the radius of the asteroids:
Now let´s plug in the values we know:
mutual gravitational attraction force
gravitational constant
Solve for r and multiply by 2 because 2r = diameter
Result is d = 21.81 Feet