What is the kinetic energy of a 100 kg object that is moving with a speed of 12.5m/s

Answer:

2023857702.507 m

Explanation:

Using Newton's law of gravitation:

G = gravitational constant

m_shrew = 50 g

m_elephant = 5 × 10^3 kg

r_earth = Earth's radius, 6400 km or 6,400,000 m

m_earth = Earth's mass

Equate the gravitational forces:

G m_shrew m_earth / r_earth^2 = G m_elephant m_earth / r^2

Cancel common terms on both sides:

m_shrew / r_earth^2 = m_elephant / r^2

Rearranged to solve for r^2:

r^2 = (m_elephant × r_earth^2) / m_shrew

Substituting the values:

r^2 = 4.096 × 10^{13}

Taking square root gives:

r = 2,023,857,702.507 m

Response:

Explanation:

Torque is defined as:

where

F is the force's magnitude,

d represents the distance from where the force is applied to the center of rotation,

and is the angle between the force's direction and d.

In this question, we have:

, the force

, the distance of applying the force from the center (0,0)

, and the angle between the force's direction and a.

Thus, the torque is

Answer:

10.4 m/s

Explanation:

To solve this problem, we can apply the following SUVAT equation:

where

v denotes the final velocity

a stands for acceleration

t denotes time

For the diver in our case, the values are:

By substituting t = 1.7 s, we can find the velocity at the moment the diver strikes the water:

The negative sign indicates a downward direction; hence, the diving speed will be 10.4 m/s.

Answer:

The distance measures

Explanation:

According to the problem statement,

The box's width is

There is a gap of length

The first spring's natural length is

The spring constant for the first spring is

The second spring has a natural length of

The second spring's spring constant is

We denote the distance from the center of the box to the left edge as x.

At equilibrium,

The force exerted by the first spring is

while the force from the second spring is

Thus, at equilibrium,

Substituting values gives us

which leads to

resulting in

and finally,

this simplifies to