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The frequency of a person's pendulum is 0.3204 Hz when at a location where g is known to be exactly 9.800 m/s^2.

wel

Answer:

A) g = 9.751 m/s², B) h = 2.573 10⁴ m

Explanation:

The angular velocity of a pendulum is

w = √ g / L

Angular velocity and frequency are related.

w = 2π f

f = 1 / 2π √ g / L

A) with the initial data we can look for the pendulum length

L = 1 /4π² g / f²

L = 1 /4π² 9,800 / 0.3204²

L = 2.4181 m

The length of the pendulum does not change, let's look for the value of g for the new location

g = 4π² f² L

g = 4π² 0.3196² 2.4181

g = 9.75096 m / s²

g = 9.751 m/s²

B) The value of the acceleration of gravity can be found with the law of universal gravitation

F = G m M / $R_{e}$ ²

And Newton's second law

W = m g

W = F

G m M / $R_{e}$ ² = mg

g = G M / $R_{e}$ ²

$R_{e}$ ² = G M / g

Let's calculate

$R_{e}$ ² = 6.67 10⁻¹¹ 5.98 10²⁴ /9.75096

R = √ 4.0905 10¹³ = √ 40.9053 10¹²

R = 6.395726 10⁶ m

The height above sea level is

h = R - [tex]R_{e}[/tex

h = (6.395726 -6.37) 10⁶

h = 0.0257256 106

h = 2.573 10⁴ m

7 0

4 years ago

A child with a mass of 23 kg rides a bike with a mass of 5.5 kg at a velocity of 4.5 m/s to the south. Compare the momentum of t

serg [7]

Answer:

Explanation:

Given the following data;

Mass of child = 23 kg

Mass of bike = 5.5 kg

Velocity = 4.5 m/s

Momentum can be defined as the multiplication (product) of the mass possessed by an object and its velocity. Momentum is considered to be a vector quantity because it has both magnitude and direction.

Mathematically, momentum is given by the formula;

$Momentum = mass * velocity$

To find the momentum of each of them;

I. Momentum of the child

Momentum C = mass * velocity

Momentum C = 23 * 4.5

Momentum C = 103.5 Kgm/s

II. Momentum of the bike

Momentum B = mass * velocity

Momentum B = 5.5 * 4.5

Momentum B = 24.75 Kgm/s

Hence, we can deduce from the calculations that the momentum of the child is greater than that of the bike because of the higher mass possessed by the child.

4 0

3 years ago

Suppose the maximum power delivered by a car's engine results in a force of 16000 N on the car by the road. In the absence of an

joja [24]

Answer:

Approximately $9.7\; \rm m \cdot s^{-2}$ .

Explanation:

Assuming that there is no other force on this vehicle, the $16000\; \rm N$ force from the road would be the only force on this vehicle. The net force would then be equal to this $16000\; \rm N\!$ force. The size of the net force would be $16000\; \rm N\!\!$ .

Let $m$ denote the mass of this vehicle and let $\Sigma F$ denote the net force on this vehicle.

By Newton's Second Law of motion, the acceleration of this vehicle would be proportional to the net force on this vehicle. In other words, the acceleration of this vehicle, $a$ , would be:

$\begin{aligned}a &= \frac{\Sigma F}{m}\end{aligned}$ .

For this vehicle, $\Sigma F = 16000\; \rm N$ whereas $m = 1650\; \rm kg$ . The acceleration of this vehicle would be:

$\begin{aligned}a &= \frac{16000\; \rm N}{1650\; \rm kg} \\ &= \frac{16000\; \rm kg \cdot m\cdot s^{-2}}{1650\; \rm kg}\\ &\approx 9.7 \; \rm m \cdot s^{-2}\end{aligned}$ .