Answer:
vi = 4.77 ft/s
Explanation:
Given:
- The radius of the surface R = 1.45 ft
- The Angle at which the the sphere leaves
- Initial velocity vi
- Final velocity vf
Find:
Determine the sphere's initial speed.
Solution:
- Newton's second law of motion in centripetal direction is given as:
m*g*cos(θ) - N = m*v^2 / R
Where, m: mass of sphere
g: Gravitational Acceleration
θ: Angle with the vertical
N: Normal contact force.
- The sphere leaves surface at θ = 34°. The Normal contact is N = 0. Then we have:
m*g*cos(θ) - 0 = m*vf^2 / R
g*cos(θ) = vf^2 / R
vf^2 = R*g*cos(θ)
vf^2 = 1.45*32.2*cos(34)
vf^2 = 38.708 ft/s
- Using conservation of energy for initial release point and point where sphere leaves cylinder:
ΔK.E = ΔP.E
0.5*m* ( vf^2 - vi^2 ) = m*g*(R - R*cos(θ))
( vf^2 - vi^2 ) = 2*g*R*( 1 - cos(θ))
vi^2 = vf^2 - 2*g*R*( 1 - cos(θ))
vi^2 = 38.708 - 2*32.2*1.45*(1-cos(34))
vi^2 = 22.744
vi = 4.77 ft/s
Answer: D
Explanation:
When an object falls gravity is pulling down on it and is picking up speed, but as it gains speed air resistance becomes a faster. Air resistance increases with speed. And that force keeps it from accelerating eventually the object will pick up speed such that the force due to air resistance will keep it from getting any more speed at that point force due to air resistance is equal to its weight (mg) and the net force is equal to zero so it won’t accelerate any more at that point it is said to be moving in terminal velocity.
When an object has reached terminal velocity, it will have a constant velocity
Answer:
1. 1 s = 1 x 10⁶ μs
2. 1 g = 0.001 kg
3. 1 km = 1000 m
4. 1 mm = 1 x 10⁻³ m
5. 1 mL = 1 x 10⁻³ L
6. 1 g = 100 dg
7. 1 cm = 1 x 10⁻² m
8. 1 ms = 1 x 10⁻³ s
Explanation:
1.
1 x 10⁻⁶ s = 1 μs
(1 x 10⁻⁶ x 10⁶) s = 1 x 10⁶ μs
<u>1 s = 1 x 10⁶ μs</u>
2.
1000 g = 1 kg
1 g = 1/1000 kg
<u>1 g = 0.001 kg</u>
3.
<u>1 km = 1000 m</u>
<u></u>
4.
<u>1 mm = 1 x 10⁻³ m</u>
<u></u>
5.
<u>1 mL = 1 x 10⁻³ L</u>
<u></u>
6.
1 x 10⁻² g = 1 dg
(1 x 10⁻² x 10²) g = 1 x 10² dg
<u>1 g = 100 dg</u>
<u></u>
7.
<u>1 cm = 1 x 10⁻² m</u>
<u></u>
8.
<u>1 ms = 1 x 10⁻³ s</u>
Given :
Vector A has a magnitude of 63 units and points west, while vector B has the same magnitude and points due south.
To Find :
The magnitude and direction of
a) A + B .
b) A - B.
Solution :
Let , direction in north is given by +j and east is given by +i .
So , 
and 
Now , A + B is given by :
Direction of A+B is 45° north of west .
Also , for A-B :
Direction of A-B is 45° south of west .
( When two vector of same magnitude which are perpendicular to each other are added or subtracted the resultant is always 45° from each of them)
Hence , this is the required solution .
Answer:
2000 nickels
Explanation:
One way to solve proportionality problems, direct and inverse: the simple 3 rule.
If the relationship between the magnitudes is direct (when one magnitude increases so does the other), the simple direct rule of three must be applied.
On the contrary, if the relationship between the magnitudes is inverse (when one magnitude increases the other decreases) the rule of three simple inverse applies.
The simple 3 rule is an operation that helps us quickly solve proportionality problems, both direct and inverse.
To make a simple rule of three we need 3 data: two magnitudes proportional to each other, and a third magnitude. From these, we will find out the fourth term of proportionality.
In the simple three rule, therefore, the proportionality relationship between two known values A and B is established, and knowing a third value C, a fourth value D is calculated.
A -> B
C -> D
Calculation
1 nickel --> 5 g
X? nickel --> 10000g
X = (10000 g * 1 nickel) / 5 g
X = 2000 nickels
