Explain how a bathroom scale is like a biofeedback machine.

A 10 kg mass stretches a spring 70 cm in equilibrium. Suppose a 2 kg mass is attached to the spring, initially displaced 25 cm b

NARA [144]

Answer:

Explanation:

1. Find spring constant k. From a free body diagram, you will get the forces on the 10 kg mass, with a displacement d. It will be gravity pulling the mass down and the spring force pulling the mass up. The 10 kg mass is in equilibrium. The resulting equation will be:

$F = m_1a = kd - m_1g = 0 => m_1g = kd => k = \frac{m_1g}{d}$

2. Use the result from 1. to find the equations of motion. In general they are given by:

$x(t) = Acos(\omega t + \phi), v(t) = -\omega Asin(\omega t + \phi)$ , where ω is: $\omega = \sqrt{\frac{k}{m_2}}=\sqrt{\frac{m_1g}{m_2d}}$

To find the amplitude A and the phase angle Ф, use the given initial conditions:

m₂ = 2 kg, x(0) = -0.25 m, v(0) = 2m/s

$-0.25 = Acos(\phi)\\2 = -\omega Asin(\phi)= -\sqrt{\frac{m_1g}{m_2d}}Asin(\phi)\\-0.24 = Asin(\phi)$

Solving for Ф:

$\frac{0.24}{0.25}=tan(\phi) => \phi = 0.76$

Solving for A:

$-0.25 = Acos(\phi) => A = -\frac{0.25}{cos(\phi)}=-0.35$

The equation for x(t) is now:

$x(t) = -0.35 cos(\sqrt{\frac{m_1g}{m_2d}t} +0.76)$

The frequency f is given by: $f = \frac{\omega}{2\pi}$

The period T is given by: $T = \frac{2\pi}{\omega}$

8 0

3 years ago

An athlete completes one round of a circular track of diameter 200 m in 40 s. What will be the distance covered and the displace

Zepler [3.9K]

Answer:

Explanation:

Displacement is the shortest distance possible between initial and final position.

As the athlete is in circular motion , displacement is zero. [ THis is because , the initial and final position is the same ]

Distance covered in 1 round = Circumference of the circle

Circumference of the circle = 2πr

Diameter = 200 m

Radius = 100 m

Distance covered in 1 round[ 40 sec ] = 2 × 22/7 × 100 = 628.57 m

Distance covered in 1 sec = 628.57 ÷ 40 = 15.71 m

2min 20 sec = 140 sec

Distance covered in 140 sec = 15.71 × 140 = 2199.4 m

For each complete round the displacement is zero. Therefore for 3 complete rounds, the displacement will be zero.

At the end of his motion, the athlete will be in the diametrically opposite position. That is, displacement = diameter = 200 m.

Hence, the distance covered is 2200 m and the displacement is 200 m.

5 0

3 years ago

What causes a material to be classified as ferromagnetic?

denpristay [2]

Answer:

A material displaying ferromagnetism, such as the various forms of iron, steel, cobalt, nickel, and their alloys.

Explanation:

4 0

3 years ago

You are driving your car and the traffic light ahead turns red.You apply the breaks for 3s and the velocity of the car decreases

hammer [34]

Answer:

The car's displacement during this time is 25.65 meters.

Explanation:

Given that,

Final velocity of the car, v = 4.5 m/s

Deceleration of the car, $a=-2.7\ m/s^2$

Let u is the initial speed of the car. It is given by :

$v=u+at$

$u=v-at$

$u=4.5-(-2.7)\times 3$

u = 12.6 m/s

Let d is the car's displacement during this time. It can be calculated using second equation of motion as :

$d=ut+\dfrac{1}{2}at^2$

$d=12.6\times 3+\dfrac{1}{2}\times (-2.7)\times 3^2$

d = 25.65 meters

So, the car's displacement during this time is 25.65 meters. Hence, this is the required solution.

7 0

3 years ago

which of the seasons is celebrated by many northern cultures with festivals, often symbolizing rebirth?

tensa zangetsu [6.8K]

I’m not entirely certain, but usually, spring symbolizes rebirth.

4 0

3 years ago

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