The frequency can be defined as the inverse of the period, that is, it can be expressed as
Here,
T = Period
f = Frequency
For each value we only need to replace the value and do the calculation:
PART A)
T = 0.0166s
PART B)
PART C)
PART D)
Answer:
The acceleration of the ball's center of mass = 2.94 m/s²
Explanation:
The speed of the ball at the base of the ramp, v = 2.63 m/s
Mass of the ball = 1.75 kg
Radius of the ball, R = 40 cm = 0.4 m
In this motion, potential energy due to the height of the ball is converted to linear angular kinetic energy
Based on the law of energy conservation
Potential energy = Linear KE + angular KE
KE = kinetic Energy
Linear KE = 0.5 mv²
Linear KE = 0.5 * 1.75 * 2.63²
Linear KE = 6.052 J
Angular KE = 0.5 Iω²
I = 2/ 3 MR² = 0.667 * 1.75 * 0.4²
I = 0.187 N.s
ω = V/R = 2.63/0.4
ω = 6.575 Rad/s
Angular KE = 0.5 * 0.187 * 6.575²
Angular KE = 4.04 J
PE = mgh = 1.75 * 9.8 * h = 17.15h
Using the law of energy conservation
17.15h = 6.052 + 4.04
h = 10.092/17.15
h = 0.589 m
Using the equation of motion
Answer:
The total momentum after the collision is 1 kg-m/s.
Explanation:
We have,
Mass of a steel sphere is 0.5 kg
It is travelling with a speed of 2 m/s
It collides with an identical sphere at rest.
The law of conservation of momentum states that the initial momentum is equal to the final momentum for an isolated system. Here, initial momentum is :
So, the total momentum after the collision is 1 kg-m/s.
D. Geosphere (Rock)
Atmosphere (Air)
Hydrosphere (Water)
Biosphere ( Living Things)
Answer:
The answer to the question is
At the instant she loses contact with the snowball, the angle (alpha) a radial line from the center of the snowball to the skier make with the vertical is 48.2 °
Explanation:
At the point where the skier loses contact with the snpwball we have the centripetal force given by
m·g·cos θ - N =
Where N = 0 at the point the skier leaves the snowball
That is
m·g·cos θ =
The height from which the skier drops from the snowball is given by
h = r - r·cosθ
Therefore the potential energy of the skier just before leaveing the snowball is
m·g·h = m·g·r·(1-cosθ)
From conservation of energy, the total energy of the skier is constant which means that is the potential energy is transformed to kinetic energy of the form
PE = KE That is
= m·g·r·(1-cosθ) or
= 2·m·g·(1-cosθ) Howerver since
m·g·cos θ = then we have
m·g·cos θ = 2·m·g·(1-cosθ) which gives
cosθ = 2·(1-cosθ) or 3·cosθ = 2
or cosθ = and θ = = 48.1896851 °
≈48.2 °