Answer:
The frequency of the oscillation is 2.45 Hz.
Explanation:
Given;
mass of the spring, m = 0.5 kg
total mechanical energy of the spring, E = 12 J
Determine the spring constant, k as follows;
E = ¹/₂kA²
kA² = 2E
k = (2E) / (A²)
k = (2 x 12) / (0.45²)
k = 118.519 N/m
Determine the angular frequency, ω;

Determine the frequency of the oscillation;
ω = 2πf
f = (ω) / (2π)
f = (15.396) / (2π)
f = 2.45 Hz
Therefore, the frequency of the oscillation is 2.45 Hz.
Answer:
D
Explanation:
This will not change the weight and therefore not change the inertia
S.G. or specific gravity is the ratio of the density of an object to a fluid. It also is the fraction of the object's volume that would be submerged if the object were placed in the fluid. (note: if S.G.>1, the object will sink)
S.G. = density(wood) / density(water)
2/3 = density(wood) / 1000
density(wood) = 2000/3 kg/m^3 = ~666.67 kg/m^3
S.G. = density(wood) / density(oil)
9/10 = 2000/3 / density(oil)
density(oil) = 2000/3 / 9/10 = 20000/27 kg/m^3 = ~740.74 kg/m^3
Answer:
The loop penetrate 4 cm into the magnetic field.
Explanation:
Given that,
Width w= 5 cm
Length L= 10 cm
mass m = 40 g
Resistance R = 20 mΩ
Initial velocity = 1 m/s
Magnetic field = 2 T
We need to calculate the induced emf
Using formula of emf

Put the value into the formula


We need to calculate the current
Using Lenz's formula



We need to calculate the force
Using formula of force


Put the value into the formula


We need to calculate the acceleration
Using formula of acceleration

Put the value in to the formula


We need to calculate the distance
Using equation of motion





Hence, The loop penetrate 4 cm into the magnetic field.
Answer:
22kj
Explanation:
set h = 0 at the end of slide.
final height is -12m
initial condition will be Ui = 0
Ki = 1/2mv² = 1/2 x 61 x (27)² = 22234.5J
Final condition is Ui = mgh = 61 x 9.8 x -12 = -7173J
Ki = 1/2mv²
Ki= 1/2 x 61 x (16)² = 7808J
conservation energy says that
Ui + Ki = Uf +Kf +ΔEth
so ΔEth = Ui + Ki - Uf - Kf
ΔEth = 22234.5 - 7808 + 7173
ΔEth = 21600J
ΔEth =22Kj