Which choice BEST represents the sound waves that a crowd hears as they watch a team of jet fighters fly from the distance, imme
diately overhead and then off into the distance again?
1 answer:
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Answer:
1) a. 52.41 m/s
b. The skier will be going 15.35 m/s slower
2) 103.68 m
3) 35,127 J
4) a. 88.825 kJ
(b) 16.36 %
5) 3,071.12 J
Explanation:
1) a. The given height of the hill, h = 140.0 m
The mass of the skier at the top of the hill, m = 85.0 kg
The acceleration due to gravity, g = 9.81 m/s²
The initial potential energy, P.E of the skier = m×g×h = 85.0×140.0×9.81 = 116739 J
From the principle of conservation of energy, we have;
The potential energy, P.E. lost = The gain in kinetic energy, K.E.
m×g×h = 1/2×m×v²
116739 J = 1/2×85.0×v²
v² = 116739/(1/2*85.0)= 2746.8 m²/s²
v = √(2746.8 m²/s²) = 52.41 m/s
b. From 70 m up, we have;
The initial potential energy, P.E., of the skier is now = 85.0×70×9.81 = 58,369.5 J
The potential energy, P.E. lost = The gain in kinetic energy, K.E.
58,369.5 J = 1/2×85.0×v²
v² = 58,369.5/(1/2*85.0) = 1373.4 m²/s²
v = 37.06 m/s
The skier will be going 52.41 - 37.06 = 15.35 m/s slower
The skier will be going 15.35 m/s slower
2) From the principle of conservation of energy, the amount of work done (energy used) = The (potential) energy gained by the load
The amount of work done by the electric hoist = 356,000 J
The mass of the load = 350.0 kg
The height to which the load is raised = h
The potential energy gained by the load = m×g×h = 350.0×9.81×h
356,000 J = 350.0×9.81×h
h = 356,000/(350.0*9.81) = 103.68 m
The height to which the load is lifted= 103.68 m
3) The initial potential energy of the roller coaster cart = 600*35.0*9.81 = 206010 J
The final potential energy = 600*28.0*9.81= 164808 J
The velocity at point 3 = 4.5 m/s
The kinetic energy at point 3 = 1/2*600*4.5^2 = 6075 J
The total energy at point 3 = 164808 + 6075 = 170,883 J
The energy loss = The initial potential energy at point 1 - Total energy at point 3
The energy loss = 206010 - 170,883 = 35,127 J
The heat energy due to friction that must have been produced between points 1 and 3 = 35,127 J
4) a. The heat energy absorbed = mass × specific heat capacity for water, × Temperature change
The mass of the water = 2.5×10² g = 0.25 kg
= 4,180 J/(kg·°C)
Initial temperature = 10.0°C
Final temperature = 95°C
The temperature change = 95.0°C - 10.0°C = 85.0°C
The heat energy absorbed = 0.25*4,180* 85 = 88,825 J = 88.825 kJ
(b) The percentage efficiency = (Heat absorbed/(Heat supplied)) × 100
The heat supplied = 543 kJ
The efficiency = (88.825/543) × 100 = 16.36 %
5) The mass of the box = 115 kg
Force acting on the rope = 255 N
The angle of inclination of the force to the horizontal = 24.5°
The distance the box is displaced = 15.0 m to the right
The work done = Force applied × distance moved in the direction of the force
The work done = Force applied × distance moved in the direction of the force
Given that the load moves a distance 15.0 m to the right,we have;
The component of the force acting in the direction of the movement of the load (to the right) is 225 × cos(24.5°) = 204.74 N
The work done = 204.7*15 = 3071.12 J
The amount of work done = 3,071.12 J
Answer:
(a). The acceleration is 8.3 rad/s².
(b). The time is 3.0 sec.
Explanation:
Given that,
Rotation = 20.0 times
Time = 5.00 sec
We need to calculate the angular frequency
Using formula of angular frequency
put the value into the formula
We need to calculate the angular displacement
Using formula of angular displacement
We need to calculate the angular acceleration
Using equation of angular motion
Negative sign shows the opposite direction of the motion.
The acceleration is 8.3 rad/s².
We need to calculate the time
Using equation of angular motion
The time is 3.0 sec.
Hence, (a). The acceleration is 8.3 rad/s².
(b). The time is 3.0 sec.