According to Newton's second law, the resultant of the forces acting on the box is equal to the product between its mass and its acceleration:
(1)
we are only concerned about the horizontal direction, so there are only two forces acting on the box in this direction:
- the horizontal component of the force exerted by the rope, which is equal to
- the frictional force, acting in the opposite direction, which is equal to
By applying Newton's law (1), we can calculate the acceleration of the box:
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 / ²
And Newton's second law
W = m g
W = F
G m M / ² = mg
g = G M / ²
² = G M / g
Let's calculate
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
Answer:
Speed will be 30810 rpm
Explanation:
We have given diameter of the tire d = 24 inch
So radius
We have given linear velocity v = 35 mph
We know that linear velocity is given by
As we know that 1 mile = 63360 inch and 1 hour = 60 min
Answer:
0.00899 N
Explanation:
The magnitude of the electrostatic force between two charges is given by the equation:
where:
is the Coulomb's constant
are the charges
r is the distance between the two charges
And the force is:
- Repulsive if the two charges have same sign
- Attractive if the two charges have opposite sign
In this problem we have:
(charge of object 1)
(charge of object 2)
r = 1 m (separation between the objects)
So, the electric force is