Answer:
K.E₂ = mg(h - 2R)
Explanation:
The diagram of the car at the top of the loop is given below. Considering the initial position of the car and the final position as the top of the loop. We apply law of conservation of energy:
K.E₁ + P.E₁ = K.E₂ + P.E₂
where,
K.E₁ = Initial Kinetic Energy = (1/2)mv² = (1/2)m(0 m/s)² = 0 (car initially at rest)
P.E₁ = Initial Potential Energy = mgh
K.E₂ = Final Kinetic Energy at the top of the loop = ?
P.E₂ = Final Potential Energy = mg(2R) (since, the height at top of loop is 2R)
Therefore,
0 + mgh = K.E₂ + mg(2R)
<u>K.E₂ = mg(h - 2R)</u>
Answer:
A. The period of an oscillation does not depend upon amplitude.
Explanation:
The period of a spring-mass system is:
T = 1/f = 2π√(m/k)
where f is the frequency, m is the mass, and k is the spring constant.
The answer isn't B. There are no frictionless systems in the real world.
The answer isn't C or D. As shown, the frequency is a function of both the mass and the spring constant.
The answer isn't E. Turning motion into heat is not an advantage for a clock.
The correct answer is A. The period of the system does not depend on the amplitude.
Answer:
Explanation:
Average energy contained by a slice of pizza is 860 J .
energy used in lifting 32 kg bar by .50 m = mgh
= 32 x 9.8 x .5 = 156.8 J
efficiency is 25 % , so energy used up = .75 x 156.8 = 117.6 J
So number of times exercise to be repeated to burn off energy of a slice of pizza
= 860 / 117.6
= 7.3 or 7 times .
Answer:
1.6×10⁻⁶ N.
Explanation:
From the question,
F = (V/r)q......................... Equation 1
Where F = Electric force on the raindrop, V = Potential difference between the base of the cloud and the ground, r = distance between the base of the cloud and the ground, q = the charge on a rain drop.
Given: V = 200MV = 200×10⁶ V, r = 500 m, q = 4.0×10⁻¹² C.
Substitute these values into equation 1
F = [(200×10⁶ )/500]×4.0×10⁻¹²
F = 1.6×10⁻⁶ N.
Answer:
a. Speed = 1.6 m/s
b. Amplitude = 0.3 m
c. Speed = 1.6 m/s
Amplitude = 0.15 m
Explanation:
a.
The frequency of the wave must be equal to the reciprocal of the time taken by the boat to move from the highest point to the highest point again. This time will be twice the value of the time taken to travel from the highest point to the lowest point:
frequency = 
= 0.25 Hz
The wavelength of the wave is the distance between consecutive crests of wave. Therefore,
Wavelength = 6.4 m
Now, the speed of the wave is given as:
Speed = (Frequency)(Wavelength)
Speed = (0.25 Hz)(6.4 m)
<u>Speed = 1.6 m/s</u>
<u></u>
b.
Amplitude is the distance between the mean position of the wave and the extreme position. Hence, it will be half the distance between the highest and lowest point:
Amplitude = (0.5)(0.6 m)
<u>Amplitude = 0.3 m</u>
<u></u>
c.
frequency = = 0.25 Hz
Speed = (Frequency)(Wavelength)
Speed = (0.25 Hz)(6.4 m)
<u>Speed = 1.6 m/s</u>
<u></u>
Amplitude = (0.5)(0.3 m)
<u>Amplitude = 0.15 m</u>
