If that's the case, then
50 units = 0.55 x the input energy
Divide each side by 0.55 :
50 units/0.55 = the input energy =
<em> 90 and 10/11 units</em>
Answer:
(a) The length of the pendulum on Earth is 36.8cm
(b) The length of the pendulum on Mars is 13.5cm
(c) Mass suspended from the spring on Earth is 0.37kg
(d) Mass suspended from the spring on Mars is 0.36kg
Explanation:
Period = 1.2s, free fall acceleration on Earth = 9.8m/s^2, free fall acceleration on Mars = 3.7m/s^2
( a) Length of pendulum on Earth = [( period ÷ 2π)^2] × acceleration = (1.2 ÷ 2×3.142)^2 × 9.8 = 0.0365×9.8 = 0.358m = 35.8cm
(b) Length of the pendulum on Mars = (1.2÷2×3.142)^2 × 3.7 = 0.0365×3.7 = 0.135cm = 13.5m
(c) Mass suspended from the spring on Earth = (force constant×length in meter) ÷ acceleration = (10×0.358) ÷ 9.8 = 0.37kg
(d) Mass suspended from the spring on Mars = (10×0.135)÷3.7 = 0.36kg
3.
a)
r = distance of each mass in each hand from center = 0.6 m
m = mass of each mass in each hand = 2 kg
v = linear speed = 1.1 m/s
L = combined angular momentum of the masses = ?
Combined angular momentum of the masses is given as
L = 2 m v r
L = 2 (2) (1.1) (0.6)
L = 2.64 kg m²/s
b)
v' = linear speed when she pulls her arms = ?
r' = distance of each mass from center after she pulls her arms = 0.15 m
Using conservation of momentum , angular momentum remains same, hence
L = 2 m v' r'
2.64 = 2 (2) (0.15) v'
v' = 4.4 m/s
Answer:
g, downward
Explanation:
It is given that, a baseball is thrown straight upward. The force acting on the stone is force of gravity. It is moving under the action of gravity. We know that the force of gravity always acts in a downward direction.
At the highest point, the velocity of the stone will be equal to 0. It will move will constant acceleration equal to g and it always acts in downward direction.
Hence, the correct option is (e) "downward direction".
Answer:
t = 3.414 s
s = 23.3 m
Explanation:
Let t be the total time of motion
Let s be the total distance of motion
s - s/2 = ½at² - ½a(t - 1²) = ½a(t² - (t - 1)²)
s/2 = ½a(t² - (t² - 2t + 1)) = ½a(t² - t² + 2t - 1)
s = a(2t - 1)
s = 4(2t - 1)
s = 8t - 4
8t - 4 = ½4t²
8t - 4 = 2t²
0 = 2t² - 8t + 4
0 = t² - 4t + 2
t = (4 ±√(4² - 4(1)(2))) / 2 = (4 ± √8)/2 = 2 ± √2
t = 3.414 s
or
t = 0.5857... s which we ignore because it does not have a full last second.
s = ½(4)3.414² = 23.3137... 23.3 m
