Answer:
The magnitude of gravitational force between two masses is 
.
Explanation:
Given that,
Mass of first lead ball, 
Mass of the other lead ball, 
The center of a large ball is separated by 0.057 m from the center of a small ball, r = 0.057 m
We need to find the magnitude of the gravitational force between the masses. It is given by the formula of the gravitational force. It is given by :
So, the magnitude of gravitational force between two masses is . Hence, this is the required solution.
Answer:
4.4 square meters = 47 square foot
Explanation:
We have
1 meter = 3.28084 foot
1 square meter = 3.28084 x 3.28084 square foot = 10.76 square foot
4.4 square meters = 4.4 x 10.76 = 47.36 square foot = 47 square foot
4.4 square meters = 47 square foot
a) 1.48 m/s
The tuning fork is moving by simple harmonic motion: so, the maximum speed of the tip of the prong is related to the frequency and the amplitude by
where
is the maximum speed
is the angular frequency
A is the amplitude
For the tuning fork in the problem, we have
, where f is the frequency
is the amplitude
Therefore, the maximum speed is
b) 
The fly's maximum kinetic energy is given by
where
is the mass of the fly
is the maximum speed
Substituting into the equation, we find
Answer:
a) v₀ = 69.29 m / s
, b) t = 18.84 s
Explanation:
a) For this exercise we will use the projectile launch equations
x = v₀ₓ t
y = y₀ + 
t - ½ g t²
Let's fix our reference system on the volcano, so the horizontal distance x = 1 km = 1000 m and the vertical distance y = -900 m, the initial height of the crater is I = 0 m. Let's replace to find the speeds
v_{oy} = v₀ sin θ
v₀ₓ = v₀ cos θ
y = v₀ sin θ (x / v₀ cos θ) - ½ g (x / v₀ cos θ)2
y = x tan θ - ½ g x² / v₀² sec² θ
½ g x² sec² θ / v₀² = x tan θ - y
v₀² = ½ g x² sec² θ / (x tan θ –y)
Let's calculate
v₀² = ½ 9.8 1000² sec² 40 / (1000 tan 40 - (-900))
v₀ = √ (8.35 10⁶ / 1,739 10³)
v₀ = 69.29 m / s
b) Flight time
x = v₀ₓ t
t = x / v₀ cos θ
t = 1000 / 69.29 cos 40
t = 18.84 s
