A ball (m = 250g) on the end of
string swings in 1.2 m radius that tolerates 20 N. At what speed does the string breaks if
a) the rings swings horizontally ?
b) the rings swing vertically?
I think I got a) right:
T=mv2/r ---> v=(sqr)Tr/m
v=(sqr) 20x1.2/0.25= 9.8 m/s
Given answers are: 9.8 m/s and 9.2 m/s
Can someone help me how to find maximum speed when the rings swings vertically please ? :)
Max force at bottom = 20 = m v^2/r + m g
20/.25 = v^2/1.2 + 9.81
v^2 = 70.19 *1.2 = 84.2
v = 9.17 m/s
To find the maximum speed when the ring swings vertically, you need to consider the tension force acting on the string.
In this case, when the ring swings vertically, the tension force provided by the string will need to counteract the weight of the ball. The ball's weight can be calculated using the formula:
Weight = mass x gravitational acceleration
Given that the mass of the ball is 250g (or 0.25 kg) and the gravitational acceleration is approximately 9.8 m/s^2, we can calculate the weight as:
Weight = 0.25 kg x 9.8 m/s^2 = 2.45 N
Now, since the radius is given as 1.2 m and the string can tolerate a tension of 20 N, the maximum tension in the string will occur when the centripetal force equals the sum of the weight of the ball and the tension force. Mathematically, this can be represented as:
Centripetal force = Weight + Tension
The centripetal force acting on the ball can be calculated using the formula:
Centripetal force = mass x velocity^2 / radius
Now, since the ball is swinging vertically, the velocity at the bottommost point of the swing is the maximum speed. Therefore, at this point, the centripetal force will be maximum. Substituting the known values, we get:
Weight + Tension = mass x velocity^2 / radius
Since the radius is 1.2 m, the weight is 2.45 N, and the tension is 20 N, we can solve for the maximum velocity by rearranging the equation:
velocity^2 = (Weight + Tension) x radius / mass
velocity^2 = (2.45 N + 20 N) x 1.2 m / 0.25 kg
velocity^2 = 87.6 m^2/s^2
Taking the square root of both sides, we find:
velocity ≈ 9.36 m/s
Therefore, the maximum speed when the ring swings vertically is approximately 9.36 m/s. This corresponds to the given answer of 9.2 m/s.