A 200 g block on a 50 cm long string swings in a circle. It is frictionless and swings at 75 rpm.

What is its speed and the tension on the string?

** its speed and tension on string are: **
[ V = 3.925 \frac{m}{s}
F = 6.2 N ] ; The speed of the block is given by:
V = w ∗ R
Where,
w: angular speed
r: radius of the circular path.
The angular velocity must be in radians over seconds:
[ w = (75) * (2\pi) * (\frac{1}{60})
w = 7.85 ]
The radius must be in the subway:
[ R = (50) * (\frac{1}{100})
R = 0.5 m ]
Then, the speed is given by:
[ V = (7.85) * (0.5)
]
V = 3.925 s m ​
The tension of the rope is the centripetal force.
By definition, the centripetal force is:
F = m ∗ ( R V 2 ​ )
Where,
m: mass of the block in kilograms
Substituting values:
[ F = 0.2 * (\frac{3.925 ^ 2}{0.5})
F = 6.2 N ]

Answered by carlosego | 2024-06-24

angular velocity = (75x2pie)/60 =2.5pie ras^-1 linear velocity(or speed) at end of string, v = radius x angular velocity v= 0.5 x 2.5pie v=3.93 ms^-1
tension of string (I beleve is centeral force aplied by string), F= (mv^2)/r F= (0.2 x 3.93^2)/0.5 F=6.18 N (sorry if wrong)

Answered by jackattackblunt | 2024-06-24

The speed of the block is approximately 3.925 m/s, and the tension in the string is about 6.16 N. This is calculated using angular speed conversion and centripetal force equations. These principles are fundamental in understanding circular motion.
;

Answered by carlosego | 2024-09-26