A ball of mass 200 grams is whirled in a circle at the end of a strong 100 cm long rope whose breaking strength is 10 N. Neglecting gravity, the maximum speed of the ball is approximately.
To find the maximum speed of the ball, we need to consider the forces acting on it. In this case, we have the centripetal force provided by the tension in the rope.
The centripetal force (Fc) is given by the equation:
Fc = (mv^2) / r
Where:
m = mass of the ball
v = velocity of the ball
r = radius of the circular path
In this case, the radius of the circular path is equal to the length of the rope, which is 100 cm.
Converting the radius to meters:
r = 100 cm = 1 meter
We can rearrange the equation to solve for the velocity:
v = sqrt((Fc * r) / m)
To find the maximum speed of the ball, we need to determine the maximum centripetal force that the rope can withstand without breaking.
Considering that the breaking strength of the rope is 10 N, the maximum centripetal force is 10 N.
Now we can substitute the values into the equation:
v = sqrt((10 N * 1 meter) / (200 grams))
Converting the mass to kilograms:
m = 200 grams = 0.2 kg
v = sqrt((10 N * 1 meter) / (0.2 kg))
v = sqrt(50 m^2 / s^2)
v = 7.07 m/s (approximately)
Therefore, the maximum speed of the ball is approximately 7.07 m/s.
To calculate the maximum speed of the ball, we can use the concept of centripetal force.
The centripetal force is the force required to keep an object moving in a circular path. It is given by the formula:
F = (m * v^2) / r
where F is the centripetal force, m is the mass of the object, v is the velocity of the object, and r is the radius of the circular path.
In this case, we want to find the maximum speed of the ball, which occurs when the tension in the rope is equal to its breaking strength. This means the centripetal force is equal to the breaking strength of the rope.
Therefore, we can set F equal to 10 N:
10 = (0.2 * v^2) / 1
Now, let's solve for v:
v^2 = (10 * 1) / 0.2
v^2 = 50
v = √50
v ≈ 7.07 m/s
So, the maximum speed of the ball is approximately 7.07 m/s.