A ship starting from rest (a floating position achieved at the instant before th

Question

A ship starting from rest (a floating position achieved at the instant before the anchors fully retract), travels on a circular arc or path that has a radius of 3000km. When the engine turns on, the ship quickly reaches a maximum speed of 10km/s and then enters the circular path at which time the engines are turned off again. During the time that the ship spends along the path, it experiences a constant tangential deceleration equal to 10m/s2 to fluid resistance.

a) When does the ship stop moving along the circular path?

b) What is the angular distance traveled in radians?

c) At an instant where t= 1/2 (time it takes the ship to stop moving), what is the magnitude of the ship's net acceleration?

Explanation / Answer

a) Intial velocity =u = 10000 m/s

Final velocity = v = 0

aceleration = -10 m/s^2

Negative because its deceleration

using equation of motion

v = u + at

0 = 10000 - 10t

t = 1000 s

b) The relationship of linear and angular speed is given by:

v = r

Where v is the linear speed,
is the angular speed,
and r is the radius of the particle

= 10000/3000 rev/sec = 3.33 rev/sec

In radians, this becomes:
= (3.33 rev/s) × ( 2 rad/rev ) = 20.94 (rad/s)

Distance traveled is given by the conversion of this formula:
x = x' + v·t

To its angular counterpart in radians:
= ' + ·t

Reference the beginning by:
' = 0 radians
It goes on for 1000 seconds
t = 1000 sec

Solve for the traveled angle:
= (0) + (20.94 rad/s)·(1000 s)
Hence the angular distance traveled = 20943 radian

c) when t = 1/2 minute ( I have taken time in minute since unit is not given)

t = 30 s

acceleration will be

10000 +30a = 0

=> a = -10000/30 = -333.3 m/s^2

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.