A 0.65m long cord exerts a centripetal force of 11.6 N on a 0.10 kg mass tied to the end of the cord. What is the tangential and angular velocity of the mass?
11.6 = m v^2/R = 0.1 * v^2 / 0.65
so
v^2 = 75.4
v = 8.68 m/s
omega =v/R
To find the tangential velocity and angular velocity of the mass, we can use the formula for centripetal force:
F = m * v^2 / r
Where:
F is the centripetal force
m is the mass
v is the tangential velocity
r is the radius
We are given:
F = 11.6 N
m = 0.10 kg
r = 0.65 m
Rearranging the formula to solve for v:
v = sqrt(F * r / m)
Substituting the given values:
v = sqrt(11.6 * 0.65 / 0.10)
Calculating the expression inside the square root:
v = sqrt(7.54)
v ≈ 2.746 m/s
The tangential velocity of the mass is approximately 2.746 m/s.
To find the angular velocity, we can use the following formula:
ω = v / r
Where:
ω is the angular velocity
v is the tangential velocity
r is the radius
Substituting the given values:
ω = 2.746 / 0.65
ω ≈ 4.227 rad/s
The angular velocity of the mass is approximately 4.227 rad/s.
To find the tangential velocity and angular velocity of the mass, we can use the formulas related to centripetal force:
Centripetal force (F) = (mass (m) * tangential velocity (v)^2) / radius (r)
Angular velocity (ω) = tangential velocity (v) / radius (r)
Given:
Centripetal force (F) = 11.6 N
Mass (m) = 0.10 kg
Radius (r) = 0.65 m
Let's find the tangential velocity first:
Rearranging the formula for centripetal force, we have:
F = (m * v^2) / r
Multiply both sides of the equation by r:
F * r = m * v^2
Rearrange the equation to solve for v:
v^2 = (F * r) / m
Take the square root of both sides to find v:
v = √((F * r) / m)
Now, plug in the given values:
v = √((11.6 * 0.65) / 0.10)
Calculate the value:
v ≈ √75.4 ≈ 8.68 m/s
So, the tangential velocity of the mass is approximately 8.68 m/s.
Next, let's find the angular velocity (ω):
ω = v / r
Plug in the given values:
ω = 8.68 / 0.65
Calculate the value:
ω ≈ 13.36 rad/s
So, the angular velocity of the mass is approximately 13.36 rad/s.