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valentina_108 [34]

3 years ago

8

(a) Calculate the magnitude of the gravitational force exerted by Mars on a 67 kg human standing on the surface of Mars. (The ma

ss of Mars is 6.4 × 1023 kg and its radius is 3.4 × 106 m.)

1 answer:

Reptile [31]3 years ago

6 0

Answer:

2474.13 N

Explanation:

From Newton's Law of universal gravitation,

F = Gmm'/r².................... Equation 1

Where F = gravitational force, m = mass of the human, m' = mass of mars, G = Gravitational acceleration, r = radius of mars.

Given : m = 67 kg, m' = 6.4×10²³ kg, r = 3.4×10⁶ m

Constant: G = 6.67×10⁻¹¹ Nm²/kg².

Substituting into equation 1

F = 67(6.4×10²³)(6.67×10⁻¹¹)/ (3.4×10⁶)²

F = 28600.96×10¹²/11.56×10¹²

F = 2474.13 N.

Hence the gravitational force = 2474.13 N

You might be interested in

Why doesn’t a machine that increases force break the law of conservation of energy?

USPshnik [31]

Answer:

A machine in which work input equals work output. energy can be used to do work, work can be used to transfer energy. The change in the kinetic energy of an object is equal to the net work done on the object.

hope this helps

8 0

3 years ago

A swimming pool has the shape of a right circular cylinder with radius 21 feet and height 10 feet. Suppose that the pool is full

AysviL [449]

Answer:

The water required to pump all the water to a platform 2 feet above the top of the pool is is 6061310.32 foot-pound.

Explanation:

Given that,

Radius = 21 feet

Height = 10 feet

Weighing = 62.5 pounds/cubic

Work = 4329507.37572

Height = 2 feet

Let's look at a horizontal slice of water at a height of h from bottom of pool

We need to calculate the area of slice

Using formula of area

$A=\pi r^2$

Put the value into the formula

$A=\pi\times21^2$

$A=441\pi\ feet^2$

Thickness of slice $t=\Delta h\ ft$

The volume is,

$V=(441\pi\times\Delta h)\ ft^3$

We need to calculate the force

Using formula of force

$F=W\times V$

Where, W = water weight

V = volume

Put the value into the formula

$F=62.5\times(441\pi\times\Delta h)$

$F=27562.5\pi\times\Delta h\ lbs$

We need to calculate the work done

Using formula of work done

$W=F\times d$

Put the value into the formula

$W=27562.5\pi\times\Delta h\times(10-h)\ ft\ lbs$

We do this by integrating from h = 0 to h = 10

We need to find the total work,

Using formula of work done

$W=\int_{0}^{h}{W}$

Put the value into the formula

$W=\int_{0}^{10}{27562.5\pi\\times(10-h)}dh$

$W=27562.5\pi(10h-\dfrac{h^2}{2})_{0}^{10}$

$W=27562.5\pi(10\times10-\dfrac{100}{2}-0)$

$W=4329507.37572$

To pump 2 feet above platform, then each slice has to be lifted an extra 2 feet,

So, the total distance to lift slice is (12-h) instead of of 10-h

We need to calculate the water required to pump all the water to a platform 2 feet above the top of the pool

Using formula of work done

$W=\int_{0}^{h}{W}$

Put the value into the formula

$W=\int_{0}^{10}{27562.5\pi\\times(12-h)}dh$

$W=27562.5\pi(12h-\dfrac{h^2}{2})_{0}^{10}$

$W=27562.5\pi(12\times10-\dfrac{100}{2}-0)$

$W=1929375\pi$

$W=6061310.32\ foot- pound$

Hence, The water required to pump all the water to a platform 2 feet above the top of the pool is is 6061310.32 foot-pound.

8 0

3 years ago

You and your friend are both 14 years old. Your friend however moves to a planet where just 30 minutes on that planet is the sam

vaieri [72.5K]

Answer:

ok so

Explanation:

1.) 1 hour

2.) 14 years old

3.)

24 years old

4.) you are

5 0

2 years ago

Light enters a substance from air at 30 degrees to thenormal.

Gwar [14]

Answer:

Explanation:

The angle of incidence and refraction are both measured from the normal

angle of incidence = 30°

angle of refraction = 23°

refractive index(n) = sini / sinr

n = sin30°/sin23°

n = 1.27965

refractive index (n) = 1/sinC

where C is the critical angle.

sinC= 1/n

C =arcsin (1/n)

C =arcsin (1/1.27965)

C = 51.39°

5 0

3 years ago

If Karen rode her bicycle 5 km to school in 30 minutes, what was her average speed? Give your answers in km/h.

Doss [256]

Answer:

10 km/h

Explanation:

Before calculating the average speed, we need to convert the time taken for the trip from minutes to hours. Since 1 hour cointains 60 minutes, we have:

$1 h: 60 min = t : 30 min\\t=\frac{1 h \cdot 30 min}{60 min}=0.5 h$

Karen's average speed is given by:

$v=\frac{d}{t}$

where

d = 5 km is the distance covered

t = 0.5 h is the time taken for the trip

Substituting into the equation, we find

$v=\frac{5 km}{0.5 h}=10 km/h$

5 0

3 years ago