The string of a certain yo-yo is 80 cm long and will break when the force on it is 10 N. What is the highest speed the 200 g yo-yo can have when it is being whirled in a circle? Ignore the gravitational pull of the earth on the yo-yo.
M V ^2/R = 10 N.
R = 0.8 m
M = 0.200 kg
Solve for V, in m/s.
Okay, so would I solve it like:
v^2=.8/.200 ?
1.5 m/s
To find the highest speed at which the yo-yo can be whirled in a circle without the string breaking, we need to consider the relationship between centripetal force, speed, and radius.
Centripetal force is the force that keeps 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 or speed of the object
r is the radius of the circular path
In this case, we need to rearrange the formula to solve for velocity (v):
v = √((F * r) / m)
Given:
The force (F) that will break the string is 10 N.
The string length (radius, r) is 80 cm = 0.8 m.
The mass (m) of the yo-yo is 200 g = 0.2 kg.
Substituting the values into the formula:
v = √((10 * 0.8) / 0.2)
v = √(8 / 0.2)
v = √40
v ≈ 6.32 m/s
Therefore, the highest speed at which the 200 g yo-yo can be whirled in a circle without breaking the string is approximately 6.32 m/s.