A steel ball hangs in a 147cm thread which is dragged right and then let go. Velocityh of the ball is 2,44m/s when it goes through the middle position.
I don't have any mass given up.
How many degrees to the side had the ball been dragged?
ke of ball at bottom = (1/2) m (2.44)^2
= 2.98 m
Pe at top = m g h = m (9.81)(h)
so
9.81 h m = 2.98 m
h = .303 meters
h = 1.47 (1 - cos theta)
.303/1.47 = 1 - cos T
.206 = 1 - cos T
-cos T = -.794
T = 37.4 degrees
thank you very much ! i got it half the way but couldn't figure out how to finish it .
You are welcome :)
To determine the number of degrees the ball had been dragged to the side before it was released, we can use the concept of circular motion and the relationship between the velocity and the displacement of the ball.
First, let's draw a diagram to visualize the situation. We have a steel ball hanging from a thread that is 147 cm long (or 1.47 m). When the ball is dragged to the side and released, it swings back and forth like a pendulum.
Now, let's consider the middle position of the ball's swing. At this point, the ball's velocity is given as 2.44 m/s.
In circular motion, the velocity of an object can be related to its displacement by the equation:
v = ωr
where:
v is the velocity,
ω (omega) is the angular velocity, and
r is the radius of motion.
Since the thread length is the radius of motion, we can rewrite the equation as:
v = ω * 1.47 m
Now, let's solve for the angular velocity (ω):
ω = v / 1.47 m
Substituting the given velocity (2.44 m/s), we can calculate:
ω = 2.44 m/s / 1.47 m ≈ 1.65986 rad/s
The angular velocity (ω) represents the rate at which the ball rotates in radians per second. To find the number of degrees, we can convert the angular velocity to degrees per second by using the conversion factor: 1 radian = 180/π degrees.
So, the angular velocity in degrees per second is:
ω (degrees/s) = (1.65986 rad/s) * (180/π) ≈ 94.8948°/s
Now that we have the angular velocity, we need to determine the time it takes for the ball to swing from the middle position to the maximum displacement, which is the side position we are trying to find.
In a pendulum motion, the period (T) is the time it takes for the ball to complete one full swing back and forth. The period can be calculated using the formula:
T = 2π / ω
Substituting the angular velocity (ω) we found earlier:
T = 2π / (1.65986 rad/s) ≈ 3.78566 s
Since the ball starts from the middle position, it takes half the period to reach the side position. Therefore, the time (t) it takes for the ball to reach the side position is:
t = T / 2 ≈ 3.78566 s / 2 ≈ 1.89283 s
Lastly, we can find the number of degrees the ball had been dragged by multiplying the time (t) by the angular velocity in degrees per second:
Number of degrees = ω (degrees/s) * t
Substituting the values we found earlier:
Number of degrees ≈ 94.8948°/s * 1.89283 s ≈ 179.582°
Therefore, the ball had been dragged approximately 179.582 degrees to the side before it was released.