tarzan swings from a vine whose length is 10m in a vertical circle under the influence of gravity .when vine make an angle of 20 degree with the vertical then find out length of arc and centripetal force experienced at this instant when tarzan has a speed of 10m/s and weighs 980N
I do not know what length of arc you mean
R = 10
v = 10
Ac = v^2/ r = 100/10 = 10 m/s^2
m = 980/g =980/9.8 =10
so F = m a = 100 Newtons centripetal
surely you want the total force in the vine ?
980 cos 20 + F ????
To find the length of the arc and the centripetal force experienced by Tarzan while swinging from the vine, we can use some basic principles of circular motion.
First, let's find the length of the arc Tarzan travels. The length of the arc of a circle is given by the formula:
arc length = r * θ
where r is the radius of the circle (in this case, the length of the vine) and θ is the angle in radians. However, we are given the angle in degrees, so we need to convert it to radians by using the formula:
θ (in radians) = (θ (in degrees) * π) / 180
Given that the length of the vine is 10m and the angle is 20 degrees, we can now calculate the length of the arc Tarzan travels:
θ (in radians) = (20 * π) / 180 = π/9
arc length = 10 * (π/9) ≈ 3.49m
So, the length of the arc Tarzan travels is approximately 3.49m.
Next, let's find the centripetal force experienced by Tarzan. The centripetal force is given by the formula:
centripetal force = (mass * velocity^2) / radius
But since we are given Tarzan's weight (force due to gravity) instead of his mass, we need to use the formula:
centripetal force = (weight * velocity^2) / (g * radius)
where g is the acceleration due to gravity, which is approximately 9.8m/s^2.
Given that Tarzan's weight is 980N (which is equal to his mass multiplied by the acceleration due to gravity), his speed is 10m/s, and the radius is 10m, we can now calculate the centripetal force:
centripetal force = (980 * 10^2) / (9.8 * 10) = 1000N
So, the centripetal force experienced by Tarzan at this instant is 1000N.