A 0.3kg mass is attached to end of a 1.0m string.the system is whirled in horizontal circular path.if the maximum tension that the string can withstand is 350N.the maximum speed of the mass if the string not to break is?

FreshTheo

2 years ago

F=mv²/r
V²= Fr/m
V= √Fr/m

V= √350 x 1/0.3

V= √350/0.3

V=√1166.67

V= 34.157m/s

All_for_one

2 years ago

To find the maximum speed of the mass when the string does not break, you need to consider the centripetal force required to keep the mass moving in a circular path.

The formula for centripetal force is:

F = (m * v^2) / r

Where:
F = Centripetal force
m = Mass (0.3 kg)
v = Velocity (maximum speed, which we want to find)
r = Radius of the circular path (1.0 m)

We also know that the maximum tension the string can withstand is 350 N. This tension is the same as the centripetal force because it provides the inward force needed to keep the mass in circular motion without breaking the string.

So, we can set up the equation:

350 N = (0.3 kg * v^2) / 1.0 m

Now, we can solve for v:

v^2 = (350 N * 1.0 m) / 0.3 kg
v^2 = 1166.67 m^2/s^2

Now, take the square root of both sides to find the maximum speed (v):

v = √1166.67 m/s
v ≈ 34.15 m/s

So, the maximum speed of the mass for the string not to break is approximately 34.15 meters per second.