The effiency of a machine is
(output work or energy) / (input work or energy) .
For the system described in the question, that's
(123 J) / (150 J) = 0.82 = 82% .
Answer:
See the answers below
Explanation:
This problem and its respective questions can be easily solved using Newton's law of universal gravitation. Which can be calculated by means of the following expression.

where:
G = it is the universal gravitation constant. = 6.673 x 10⁻¹¹ [N*m²/kg²]
m1 = mass of the first body [kg]
m2 = mass of the second body [kg]
r = distance among the bodies [m]
a. the mass of one is doubled?
When this happens we see that the force is increased twice as well, since the mass is in the numerator of the expression.
b. The masses of both are doubled?
If both masses are doubled the force is increased to four times its original value since the terms of the masses are in the numerator of the expression.
c. The distance between them is doubled?
In this case the force is decreased to half of its original value, since the distance is in the denominator of the expression of universal gravitation.
Answer:
The total distance, side to side, that the top of the building moves during such an oscillation = 31 cm
Explanation:
Let the total side to side motion be 2A. Where A is maximum acceleration.
Now, we know know that equation for maximum acceleration is;
A = α(max) / [(2πf)^(2)]
So 2A = 2[α(max) / [(2πf)^(2)] ]
α(max) = (0.025 x 9.81) while frequency(f) from the question is 0.2Hz.
Therefore 2A = 2 [(0.025 x 9.81) / [((2π(0.2)) ^(2)] ] = 2( 0.245 / 1.58) = 0.31m or 31cm
Explanation:
It is given that,
Speed of the ball, v = 10 m/s
Initial position of ball above ground, h = 20 m
(a) Let H is the maximum height reached by the ball. It can be calculated using the conservation of energy as :


h' = 5.1 m
The maximum height above ground,
H = 5.1 + 20
H = 25.1 meters
So, the maximum height reached by the ball is 25.1 meters.
(b) The ball's speed as it passes the window on its way down is same as the initial speed i.e. 10 m/s.
Hence, this is the required solution.
Answer:
C. N/m (newtons/meter)
Explanation:
Since the equation for potential energy for a spring is PE = 1/2kx², after you know <em>k </em>and <em>x</em>, you will get an answer in Joules.
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