Answer:
122.5 N/m
Explanation:
According to the law of conservation of energy, if there is no air resistance or frictional forces, the initial elastic potential energy of the spring toy is entirely converted into gravitational potential energy when the toy reaches the highest point.
Therefore, we can write:

where the term on the left is the initial elastic potential energy while the term on the right is the gravitational potential energy, and where
k is the spring constant
x = 0.02 m is the compression of the spring
m = 0.01 kg is the mass of the toy
h = 0.25 m is the height reached by the toy
is the acceleration due to gravity
Solving for k,

The position of the first ball is

while the position of the second ball, thrown with initial velocity
, is

The time it takes for the first ball to reach the halfway point satisfies



We want the second ball to reach the same height at the same time, so that




Answer:
x_{cm} = 4.644 10⁶ m
Explanation:
The center of mass is given by the equation
= 1 /
∑
Where M_{total} is the total masses of the system,
is the distance between the particles and
is the masses of each body
Let's apply this equation to our problem
M = Me + m
M = 5.98 10²⁴ + 7.36 10²²
M = 605.36 10²² kg
Let's locate a reference system located in the center of the Earth
Let's calculate
x_{cm} = 1 / 605.36 10²² [Me 0 + 7.36 10²² 3.82 10⁸]
x_{cm} = 4.644 10⁶ m
Answer:
W = 14523.6 J
Explanation:
Given,
Mass = 3.9 Kg
Vertical height , h = 380 m
Work done against gravitational force
W = m g h
g is acceleration due to gravity
W = 3.9 x 9.8 x 380
W = 14523.6 J
Hence, the work done by the gravitational force is equal to W = 14523.6 J
Answer:
the speed of the block when it reaches point B is 14 m/s
Explanation:
Given that:
mass of the block slides = 1.5 - kg
height = 10 m
Force constant = 200 N/m
distance of rough surface patch = 20 m
coefficient of kinetic friction = 0.15
In order to determine the speed of the block when it reaches point B.
We consider the equation for the energy conservation in the system which can be represented by:






v = 14 m/s
Thus; the speed of the block when it reaches point B is 14 m/s