Tarzan swings on a vine 6.8 m long. The tension in the vine is 1200 N if he's moving at 2.9 m/s when the vine is vertical. What is his mass?
ma= T-mg
a=v²/L
m(a+g)=m(v²/L +g)=T
m=T/(v²/L +g)=
=1200/(2.9²/6.8 + 9.8)=13244 N
To find Tarzan's mass, we can use the equations of motion and the tension in the vine.
We know that the tension in the vine provides the centripetal force required for Tarzan to swing in a circular path. The centripetal force is given by the formula:
Fc = (m * v^2) / r,
where Fc is the centripetal force, m is the mass, v is the velocity, and r is the radius of the circular path.
In this case, the tension in the vine (T) is equal to the centripetal force (Fc).
Therefore, we can write the equation as:
T = (m * v^2) / r.
Plugging in the values we have:
1200 N = (m * (2.9 m/s)^2) / 6.8 m.
To solve for m, we can rearrange the equation:
m = (T * r) / v^2.
Substituting the given values:
m = (1200 N * 6.8 m) / (2.9 m/s)^2.
Calculating this, we can find Tarzan's mass.