Answer:
(a) A = 0.650 m
(b) f = 1.3368 Hz
(c) E = 17.1416 J
(d) K = 11.8835 J
U = 5.2581 J
Explanation:
Given
m = 1.15 kg
x = 0.650 cos (8.40t)
(a) the amplitude,
A = 0.650 m
(b) the frequency,
if we know that
ω = 2πf = 8.40 ⇒ f = 8.40 / (2π)
⇒ f = 1.3368 Hz
(c) the total energy,
we use the formula
E = m*ω²*A² / 2
⇒ E = (1.15)(8.40)²(0.650)² / 2
⇒ E = 17.1416 J
(d) the kinetic energy and potential energy when x = 0.360 m.
We use the formulas
K = (1/2)*m*ω²*(A² - x²) (the kinetic energy)
and
U = (1/2)*m*ω²*x² (the potential energy)
then
K = (1/2)*(1.15)*(8.40)²*((0.650)² - (0.360)²)
⇒ K = 11.8835 J
U = (1/2)*(1.15)*(8.40)²*(0.360)²
⇒ U = 5.2581 J
Answer:
(A) Q = 2.26×10⁶J
(B) ΔT = 9°C
(C)
Explanation:
We have been given the mass of the hiker, the volume of water from which we can calculate the mass knowing that the density if water is 1000kg/m³.
Evaporation is a phase change and occurs at a constant temperature. We would use the latent heat of vaporization to calculate the amount of heat evaporated.
We would then equate this to the heat change it brings about in the hiker's body and then calculate the temperature drop.
See the attachment below for full solution.
First, we write the SI prefixed. The SI unit for distance is meters.
Kilo = 10³
Mega = 10⁶
Giga = 10⁹
Terra = 10¹²
Because our value has ten to the power of 11, we will use the closest and lowest power prefix, which is giga.
1.5 x 10¹¹ / 10⁹
= 1.5 x 10² Gm or 150 Gm
Writing in kilometers, we simply repeat the procedure except we divide by 10³ this time.
1.5 x 10¹¹ / 10³
= 1.5 x 10⁸ km
Answer:
Kinetic energy is given by:
K.E. = 0.5 m v²
Susan has mass, m = 25 kg
Velocity with which Susan moves is, v = 10 m/s
Hannah has mass, m' = 30 kg
Velocity with which Hannah moves is, v' = 8.5 m/s
<u>Kinetic energy of Susan:</u>
0.5 m v² = 0.5 × 25 kg × (10 m/s)² = 1250 J
<u>Kinetic energy of Hannah:</u>
0.5 m v'² = 0.5 × 30 kg × (8.5 m/s)² = 1083.75 J
Susan's kinetic energy is <u>1250 J </u>and Hannah's kinetic energy is <u>1083.75 J</u>.
Since kinetic energy is dependent on mass and square of speed. Thus, speed has a greater effect than mass. As it is evident from the above example. Susan has greater kinetic energy due to higher speed than Hannah.