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2 answers:
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Answer:
(a) 31.75 mph
(b) 31.77 mph
Explanation:
(a) For t = 10 min = 10 / 60 = 1 / 6 hour
According to the question,
dx /dt = 15 mph
dy / dt = 28 mph
After 10 minutes
x = 1/6 x 15 = 2.5 miles
y = 1/6 x 28 = 4.67 miles
According to diagram
Differentiate both sides with respect to t.
2D dD/dt = 2 x dx/dt + 2y dy/dt
D dD/dt = x dx/dt + y dy/dt
5.3 dD/dt = 2.5 (15) + 4.67 (28)
dD/dt = 31.75 miles/hour
(b) For t = 55 minutes = 55 / 60 hours
After 55 / 60 hours
x = 55 / 60 (15) = 13.75 miles
y = 55 / 60 (28) = 25.67 miles
According to diagram
Differentiate both sides with respect to t.
2D dD/dt = 2 x dx/dt + 2y dy/dt
D dD/dt = x dx/dt + y dy/dt
29.12 dD/dt = 13.75 (15) + 25.67 (28)
dD/dt = 31.77 miles/hour
Answer:
a) The initial elastic potential energy of the block-spring system is 28.113 joules.
b) The final speed of the block is approximately 4.192 meters per second.
Explanation:
a) By applying Hooke's law and definition of work, we define the elastic potential energy (), measured in joules, by the following formula:
(1)
Where:
- Spring constant, measured in newtons per meter.
- Deformation of the spring, measured in meters.
If we know that and
, then the elastic potential energy is:
The initial elastic potential energy of the block-spring system is 28.113 joules.
b) According to the Principle of Energy Conservation, the initial elastic potential energy of the block-spring system becomes into translational kinetic energy, that is:
(2)
Where:
- Mass, measured in kilograms.
- Final speed, measured in meters per second.
Then, the final speed is cleared:
If we know that and
, then the final speed of the block is:
The final speed of the block is approximately 4.192 meters per second.