Answer:
D.) 1m/s
Explanation:
Assume the initial angle of the swing is 12.8 degree with respect to the vertical. We can calculate the vertical distance from this initial point to the lowest point by first calculate the vertical distance from this point the the pivot point:
where L is the pendulum length
The vertical distance from the lowest point to the pivot point 
is the pendulum length 2m
this means the vertical distance from this initial point to the lowest point is simply:
As the pendulum travel (vertically) from the initial point to the bottom point, its potential energy is converted to kinetic energy:
where m is the mass of the pendulum, g = 10 m/s2 is the constant gravitational acceleration, h = 0.05 is the vertical it travels, v is the pendulum velocity at the bottom, which we are trying to solve for.
The m on both sides of the equation cancel out
so D is the correct answer
Answer:
0.02585 BTU
Explanation:
Given: Spring constant, k = 270 lbf/in
Initial force, f =100 lbf
Compression, x = 1 in
Work done can be calculated as follows:
| Impedance | = √ [R² +(ωL)²]
R² = 6800² = 4.624 x 10⁷
(ωL)² = (2 · π · f · 2.3 · 10⁻³)²
= 2.0884 x 10⁻⁴ f²
| Z | = √[ (4.624 x 10⁷) + (2.0884 x 10⁻⁴ f²) ] = 1.6 x 10⁵
(1.6 x 10⁵)² = (4.624 x 10⁷) + (2.0884 x 10⁻⁴ f²)
(2.56 x 10¹⁰) - (4.624 x 10⁷) = 2.0884 x 10⁻⁴ f²
Frequency² = (2.56 x 10¹⁰ - 4.624 x 10⁷) / 2.0884 x 10⁻⁴
= 2.555 x 10¹⁰ / 2.0884 x 10⁻⁴
= 1.224 x 10¹⁴
= 122,400 GHz <== my calculation
11.1 MHz <== online impedance calculator
Obviously, I must have picked up some rounding errors
in the course of my calculation.
(3) The frictional force exerted by the floor on the box
Answer:
a) 2.43 m/s
b) 4.83 m/s
c) 0.023 m/s²
Explanation:
a) Both cars cover a distance of 510 m in 210 s. Since car A has no acceleration
Speed = Distance / Time
Velocity of car A is 2.43 m/s
t = Time taken = 210 seconds
u = Initial velocity
v = Final velocity
s = Displacement = 510 m
a = Acceleration
c)
Acceleration of car B is 0.023 m/s²
b)
Final velocity of car B is 4.83 m/s
