A 75 kg mass is attached to the end of a 5.0 m long metal string which rotates in a horizontal circular path. If the maximum force that the rod can withstand is 8500 N, what is the maximum speed the mass can attain without breaking the string?*1 point0.238 m/s2.38 m/s23.8 m/s238 m/s
Question
A 75 kg mass is attached to the end of a 5.0 m long metal string which rotates in a horizontal circular path. If the maximum force that the rod can withstand is 8500 N, what is the maximum speed the mass can attain without breaking the string?*1 point0.238 m/s2.38 m/s23.8 m/s238 m/s
Solution
The maximum force that the string can withstand is equal to the centripetal force needed to keep the mass moving in a circle. The formula for centripetal force is:
F = m * v^2 / r
where: F is the force, m is the mass, v is the velocity (or speed), and r is the radius (or length of the string).
We can rearrange this formula to solve for v:
v = sqrt(F * r / m)
Substituting the given values:
v = sqrt(8500 N * 5.0 m / 75 kg)
v = sqrt(42500 N*m / 75 kg)
v = sqrt(566.67 m^2/s^2)
v = 23.8 m/s
So, the maximum speed the mass can attain without breaking the string is 23.8 m/s.
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