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4 years ago

Prove that the acceleration due to gravity is independent tothe mass of the falling body

Physics

1 answer:

ra1l [238]4 years ago

4 0

Answer:

The force of gravity on an object increases with its mass; thus, the acceleration of gravity is constant.

Explanation:

one can prove this by plugging in values to Newton's 2nd law equation

F = ma, or by using the formula to calculate the force of gravity.

Force of Gravity = GMm/r^2

with G being the gravitational constant, M the mass of the earth, m the mass of the falling body, and r the distance from the earth's center.

Force of Gravity can be written as mg, with g being the acceleration due to gravity.

As we can see, m cancels on both sides, leaving

g = GM/r^2

Generally in physics problems, r will be treated as constant to achieve

g = 9.8m/s^2

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A 3.00 kg block moving 2.09 m/s

Talja [164]

Answer:11.64kgm/s

Explanation:

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3 years ago

If we wish to expand (x + y) 8 , what is the coefficient of x 5 y 3 ? what is the coefficient of x 3 y 5 ?

Molodets [167]

We use the binomial theorem to answer this question. Suppose we have a trinomial (a + b)ⁿ, we can determine any term to be:

[n!/(n-r)!r!] a^(r) b^(n-r)

a.) For x⁵y³, the variables are: x=a and y=b. We already know the exponents of the variables. So, we equate this with the form of the binomial theorem.

r = 5
n - r = 3
Solving for n,
n = 3 + 5 = 8

Therefore, the coefficient is equal to:
Coefficient = n!/(n-r)!r! = 8!/(8-5)!8! = 56

b.) For x³y⁵, the variables are: x=a and y=b. We already know the exponents of the variables. So, we equate this with the form of the binomial theorem.

r = 3
n - r = 5
Solving for n,
n = 5 + 3 = 8

Therefore, the coefficient is equal to:
Coefficient = n!/(n-r)!r! = 8!/(8-3)!8! = 56

7 0

3 years ago

Like the filters falling through the air, a car on the freeway represents an object with a high Reynolds number traveling throug

Goshia [24]

Answer:

ΔF=125.22 %

Explanation:

We know that drag force on the car given as

$F_D=\dfrac{1}{2}\rho C_DA v^2$

$C_D$ =Drag coefficient

A=Projected area

v=Velocity

ρ=Density

All other quantity are constant so we can say that drag force and velocity can be given as

$\dfrac{F_D_1}{F_D_2}=\dfrac{v_1^2}{v_2^2}$

Now by putting the values

$\dfrac{F_D_1}{F_D_2}=\dfrac{v_1^2}{v_2^2}$

$\dfrac{F_D_1}{F_D_2}=\dfrac{50^2}{75^2}$

$\dfrac{F_D_1}{F_D_2}=0.444$

Percentage Change in the drag force

$\Delta F=\dfrac{F_D_2-F_D_1}{F_D_1}\times 100$

$\Delta F=\dfrac{F_D_2-0.444F_D_2}{0.444F_D_2}\times 100$

$\Delta F=\dfrac{1-0.444}{0.444}\times 100$

ΔF=125.22 %

Therefore force will increase by 125.22 %.

3 0

3 years ago

Firemen are shooting a stream of water at a burning building using a high-pressure hose that shoots out the water with a speed o

Mrac [35]

Answer:

a)α= 53.13°

b)The velocity at the highest point = 15 m/s

The acceleration at the highest point = 9.8 $m/s^2$

c)h=15 m

V=18.02 m/s

Explanation:

Speed of water ,u= 25 m/s

So the horizontal component of speed u = u cos α

Given that horizontal distance cover by water in 3 s is 45 m.

So We know that in projectile motion horizontal acceleration is zero.

In horizontal direction

Distance = Velocity x time

45 = u cos α x 3

u cos α = 45

45 = 25 cos α x 3

cos α = 45/75

α= 53.13°

So the velocity at the highest point = u cos α

The velocity at the highest point = 15 m/s

The acceleration at the highest point = 9.8 $m/s^2$

Now the velocity along vertical direction(Vo) = u sin α

Vo= 25 sin 53.13°

Vo =20 m/s

$h=V_o.t-\dfrac{1}{2}gt^2$

$h=20\times 3-\dfrac{1}{2}\times 10\times 3^2$

h=15 m

So at 15 m above the ground water will strike .

The y-component of velocity after 3 sec

Vy= Vo - g t

Vy = 20 - 10 x 3

Vy= -10 m/s

The horizontal component of velocity will remain 15 m/s.

The resultant velocity

$V=\sqrt{10^2+15^2}\ m/s$

V=18.02 m/s

5 0

4 years ago

Ben and Jerry went for a drive. They decided to stop for a snack and have some ice cream. How fast did they drive on their way t

raketka [301]

Answer: B) 30 km/h

Explanation:

The speed of Ben and Jerry on their way to the store is given by

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

where

d is the distance they covered

t is the time they took

From the graph, we see that Ben and Jerry travelled for a distance of d=60 km in a time of t=2 h, so their speed is

$v=\frac{60 km}{2 h}=30 km/h$

5 0

3 years ago

Read 2 more answers

Prove that the acceleration due to gravity is independent tothe mass of the falling body​

Prove that the acceleration due to gravity is independent tothe mass of the falling body