A 225 kg red bumper car is moving at 3.0 m/s. It hits a stationary 180 kg blue bumper car. The red and blue bumper cars combine

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

To tackle this issue, we will apply the principles linked to the Doppler effect. This effect refers to the alteration in the perceived frequency of any wave when there is relative motion between the source of the waves and the observer. It can be mathematically explained as

In this case,

=frequency detected by the receiver

=frequency emitted by the source

=speed of the detector

=speed of the source

v=speed of sound waves

Substituting values yields,

Thus, the frequency that passengers would hear is 422Hz

Set the initial location of kitten A on the left side of the field (designated as point A) at the origin, running east which is the positive direction. Kitten B starts at position , while kitten A’s beginning spot is .

Kitten A moves with a velocity of , and kitten B with . Their positions over time are described by

The collision occurs when the positions are the same, i.e. when . Solving this gives

Which results in approximately 6.8 seconds, considering significant figures.

Answer:

A. Reference the figure.

B. The resultant force acting on the crate is

C. Initially, we should determine the acceleration of the crate using this kinematics equation:

The crate's mass can be derived through Newton’s Second Law:

Answer:

Explanation:

Given

The spring constant for spring A is .

The spring constant for spring B is .

If both springs undergo a displacement of .

The formula for potential energy stored in a spring is

,

where k stands for the spring constant

and x denotes the amount of compression or extension.

.

Taking the ratio of equations one and two,

.

This indicates that the potential energy in spring A amounts to half that of spring B.