(a) 392 N/m
Hook's law states that:
(1)
where
F is the force exerted on the spring
k is the spring constant
is the stretching/compression of the spring
In this problem:
- The force exerted on the spring is equal to the weight of the block attached to the spring:
- The stretching of the spring is
Solving eq.(1) for k, we find the spring constant:
(b) 17.5 cm
If a block of m = 3.0 kg is attached to the spring, the new force applied is
And so, the stretch of the spring is
And since the initial lenght of the spring is
The final length will be
Solve for Speed: 16+20=36 km in 11 hrs
Answer: speed =
3.27273 kilometers per hourTo solve for speed or rate use the formula for speed, s = d/t which means speed equals distance divided by time.
<span>speed = distance/time</span>
Answer:
Explanation:
The cannonball goes a horizontal distance of 275 m . It travels a vertical distance of 100 m
Time taken to cover vertical distance = t ,
Initial velocity u = 0
distance s = 100 m
acceleration a = 9.8 m /s²
s = ut + 1/2 g t²
100 = .5 x 9.8 x t²
t = 4.51 s
During this time it travels horizontally also uniformly so
horizontal velocity Vx = horizontal displacement / time
= 275 / 4.51 = 60.97 m /s
Vertical velocity Vy
Vy = u + gt
= 0 + 9.8 x 4.51
= 44.2 m /s
Resultant velocity
V = √ ( 44.2² + 60.97² )
= √ ( 1953.64 + 3717.34 )
= 75.3 m /s
Angle with horizontal Ф
TanФ = Vy / Vx
= 44.2 / 60.97
= .725
Ф = 36⁰ .
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Answer:
137200000 watts or 137200 kilowatts
Explanation:
The formula for power is P= dhrg
Where P = Power in watts
d = density of water (1000 kg/m^3)
h = height in meters
r = flow rate in cubic meters per second,
g = acceleration due to gravity of 9.8 m/s^2,
Plugging in the known values,
we get
P = 1000 kg/m^3 * 80 m * 175 m^3/s * 9.8 m/s^2
P = 80000 kg/m^2 * 175 m^3/s * 9.8 m/s^2
P = 14000000 kg m/s * 9.8 m/s^2
P = 137200000 kg m^2/s^3
P = 137200000 watts or 137200 kilowatts
The above figure assumes 100% efficiency which is impossible. A good efficiency would be 90% so the actual power available would be close to 0.90 * 137200 = 123480 kilowatts
