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4 years ago

1. Which mathematical representation correctly identifies impulse?

Physics

1 answer:

horsena [70]4 years ago

3 0

Answer:

1. B. Impulse = Force × Time

2. A. The momentum of each ball changes, and the total momentum stays the same

3. -55 kg·m/s

4. B. 3.5 kg

5. C. 6.3 m/s

Explanation:

1. The impulse is the momentum change of an object due to a force applied for a given period

2. Given that the objects collide, and the force of the 3 kg mass moving with 24 kg·m/s acts on the 1 kg mass while the total momentum is conserved;

The stationary ball of mass 1 kg begins to moves at certain velocity after collision and therefore changes momentum, while the velocity of the ball of mass 3.0 kg reduces and the total combined momentum of the two balls in the closed system remains the same

3. By the principle of conservation of linear momentum, we have;

The sum of the momentum before the collision = The sum of the momentum after collision

Given that the objects move together after the collision, the total momentum is therefore;

Total momentum = 110 kg·m/s + -65 kg·m/s + -100 kg·m/s = 110 kg·m/s - 65 kg·m/s - 100 kg·m/s = -55kg·m/s

4. Given that the final velocity of the two objects (m₁ + m₂) combined = 50 m/s

Where;

m₁ = The mass of the first object

m₂ = The mass of the second object

The total momentum of the system = 250 kg·m/s

From momentum = Mass × Velocity, we have;

Mass = Momentum/Velocity = 250 kg·m/s/(50 m/s) = 5.0 kg

The mass (m₁ + m₂) = 5.0 kg

Given that m₁ = 1.5 kg, we have;

m₂ = 5.0 kg - m₁ = 5.0 kg - 1.5 kg = 3.5 kg

The mass of the second object = 3.5 kg

5. The mass of the cue stick = 0.5 kg

The velocity of the cue stick = 2.5 m/s

The mass of the ball = 0.2 kg

The initial velocity of the ball = 0 m/s

Given that total initial momentum = Total final momentum, we have;

0.5 kg × 2.5 m/s + 0.2 kg × 0 = 0.2 kg × v + 0.5 kg × 0

0.5 kg × 2.5 m/s = 0.2 kg × v

v = (0.5 kg × 2.5 m/s)/(0.2 kg) = 6.25 m/s ≈ 6.3 m/s

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A particle with a mass of 0.500 kg is attached to a horizontal spring with a force constant of 50.0 N/m. At the moment t = 0, th

svp [43]

a) $x(t)=2.0 sin (10 t) [m]$

The equation which gives the position of a simple harmonic oscillator is:

$x(t)= A sin (\omega t)$

where

A is the amplitude

$\omega=\sqrt{\frac{k}{m}}$ is the angular frequency, with k being the spring constant and m the mass

t is the time

Let's start by calculating the angular frequency:

$\omega=\sqrt{\frac{k}{m}}=\sqrt{\frac{50.0 N/m}{0.500 kg}}=10 rad/s$

The amplitude, A, can be found from the maximum velocity of the spring:

$v_{max}=\omega A\\A=\frac{v_{max}}{\omega}=\frac{20.0 m/s}{10 rad/s}=2 m$

So, the equation of motion is

$x(t)= 2.0 sin (10 t) [m]$

b) t=0.10 s, t=0.52 s

The potential energy is given by:

$U(x)=\frac{1}{2}kx^2$

While the kinetic energy is given by:

$K=\frac{1}{2}mv^2$

The velocity as a function of time t is:

$v(t)=v_{max} cos(\omega t)$

The problem asks as the time t at which U=3K, so we have:

$\frac{1}{2}kx^2 = \frac{3}{2}mv^2\\kx^2 = 3mv^2\\k (A sin (\omega t))^2 = 3m (\omega A cos(\omega t))^2\\(tan(\omega t))^2=\frac{3m\omega^2}{k}$

However, $\frac{m}{k}=\frac{1}{\omega^2}$ , so we have

$(tan(\omega t))^2=\frac{3\omega^2}{\omega^2}=3\\tan(\omega t)=\pm \sqrt{3}\\$

with two solutions:

$\omega t= \frac{\pi}{3}\\t=\frac{\pi}{3\omega}=\frac{\pi}{3(10 rad/s)}=0.10 s$

$\omega t= \frac{5\pi}{3}\\t=\frac{5\pi}{3\omega}=\frac{5\pi}{3(10 rad/s)}=0.52 s$

c) 3 seconds.

When x=0, the equation of motion is:

$0=A sin (\omega t)$

so, t=0.

When x=1.00 m, the equation of motion is:

$1=A sin(\omega t)\\sin(\omega t)=\frac{1}{A}=\frac{1}{2}\\\omega t= 30\\t=\frac{30}{\omega}=\frac{30}{10 rad/s}=3 s$

So, the time needed is 3 seconds.

d) 0.097 m

The period of the oscillator in this problem is:

$T=\frac{2\pi}{\omega}=\frac{2\pi}{10 rad/s}=0.628 s$

The period of a pendulum is:

$T=2 \pi \sqrt{\frac{L}{g}}$

where L is the length of the pendulum. By using T=0.628 s, we find

$L=\frac{T^2g}{(2\pi)^2}=\frac{(0.628 s)^2(9.8 m/s^2)}{(2\pi)^2}=0.097 m$

5 0

3 years ago

Fossils are rare because certain conditions are needed to preserve an organism in order for it to fossilize, and those condition

sladkih [1.3K]

Answer:

Explanation:

The least of the conditions that can result in fossilization would be <u>when an organism is a prey to several species.</u>

Fossils are remains or traces of organisms that have been geological preserved and a prey is an organism that is often hunted and serves as food to bigger organisms. <em>When an organism is eaten, the probability of it becoming a fossil becomes low. Unless such an organism is usually partially eaten by predators, there would not be any remains, let alone being fossilized.</em>

The correct option is D.

4 0

3 years ago

One event occurs at the origin at t equal to zero, and a second events occurs at the point x=5m along the x-axis at time with ct

Anastasy [175]

Answer:

The separation will be spacelike.

The first event can't cause the second event, as there exist an frame of reference in which both happens at the same time, in different positions, so, if there were causally connected, it will imply an instant connection, this is faster than light.

Explanation:

We can define the separation between two events (using the + - - - signature) as :

$(\Delta s )^2 = (ct_2 - c t_1 )^2 - (x_2 - x_1)^2$

where the separation will be lightlike if is equal to zero, timelike if is positive and spacelike if is negative.

For our problem

$c t_1 = 0$

$x_1 = 0$

$ct_2 = 4 \ m$

$x_2 = 5 \ m$

$(\Delta s )^2 = (4 \ m - 0 )^2 - ( 5 \ m - 0)^2$

$(\Delta s )^2 = (4 \ m )^2 - ( 5 \ m 0)^2$

$(\Delta s )^2 = 16 \ m^ 2 - 25 \ m^2$

$(\Delta s )^2 = - 9\ m^2$

So the separation will be spacelike, and the first event can't cause the second event, as there exist an frame of reference in which both happens at the same time, in different positions, so, if there were causally connected, it will imply an instant connection, this is faster than light.

8 0

4 years ago

What is the most widely accepted model of how the solar system formed? Explain how the solar system formed under this model

Degger [83]

Heliocentric model. It is the model where the sun is it the middle. and the planets are orbiting the sun like this (in order from shorter to longer). Mercury,Venus,Earth,Mars,Jupiter,Saturn,Uranus,and Neptune.

3 0

4 years ago

If the average gauge pressure in the vein is 12200 Pa, what must be the minimum height of the bag in order to infuse glucose int

Amanda [17]

Answer:

h = 1.22 m

Explanation:

Given:

Pressure in the vein = 12200 Pa

Specific gravity of the liquid = 1.02

now,

the pressure due to a fluid is given as:

P = pgh

where,

P is the pressure,

ρ is the density of fluid = specific gravity x density of water = 1.02 x 1000 kg/m³

ρ = 1020 kg/m³

g is the acceleration due to the gravity = 9.81m/s²

h is the height

thus,

h = P/pg = $\frac{12200}{1020\times 9.8}=1.22 m$

6 0

3 years ago