Tarzan (M= 75 KG) TRIES TO CROSS A RIVER BY SWIMMING FROM A 10.0 M LONG VINE. hIS SPEED AT THE BOTTOM OF THE SWING, JUST AS HE CLEARS THE WATER, IS 4.0 M/S. Tarzan DOESENT KNOW THAT THE VINE HAS A BREAKING STRENGHT OF 1.0X10N. WHAT IS THE TOTAL FORCE Tarzan EXCERTS ON THE VINE?
T =tension = m g + m v^2/R = 75( 9.81 + 4^2/10)
I suspect he is swinging, not swimming, and I have no idea what 1.0X10Newtons is.
To determine the total force Tarzan exerts on the vine, we need to consider the various forces acting on him.
1. Weight (W): The weight of Tarzan can be calculated using the formula W = m*g, where m is the mass and g is the acceleration due to gravity. In this case, m = 75 kg and g = 9.8 m/s^2.
W = 75 kg * 9.8 m/s^2 = 735 N
2. Centripetal Force (Fc): At the bottom of the swing, just as Tarzan clears the water, he is moving in a circular motion. The force required to keep him moving in a circular path is the centripetal force. It can be calculated using the formula Fc = (m * v^2) / r, where m is the mass, v is the velocity, and r is the radius of the swing. In this case, v = 4.0 m/s and r = 10.0 m.
Fc = (75 kg * (4.0 m/s)^2) / 10.0 m = 120 N
3. Force due to Breaking of Vine (Fv): The maximum force the vine can withstand is given as 1.0 * 10^10 N.
Now, to find the total force exerted by Tarzan on the vine, we need to consider the vector sum of these forces.
Total Force (Ftotal) = W + Fc + Fv
However, since the force due to breaking the vine is not provided, we cannot calculate the exact total force exerted by Tarzan on the vine. We need the breaking strength of the vine in order to compare it to the other forces and find the total force.
To find the total force Tarzan exerts on the vine, we need to consider the forces acting on him.
1. Gravitational Force (Weight):
The weight of an object is given by the formula: Weight = mass × acceleration due to gravity.
In this case, Tarzan's weight (W) can be calculated as:
W = mass × acceleration due to gravity = 75 kg × 9.8 m/s² = 735 N.
2. Centripetal Force:
When Tarzan swings on the vine, he moves in a circular motion. According to the principles of circular motion, there is a centripetal force acting towards the center of the circle. This force is given by the formula:
Centripetal Force = (mass × velocity^2)/radius.
In this case, the radius is the length of the vine, which is 10.0 m, and the velocity is 4.0 m/s.
Centripetal Force = (75 kg × (4.0 m/s)^2)/10.0 m = 120 N.
Therefore, the total force Tarzan exerts on the vine is the sum of the gravitational force and the centripetal force:
Total Force = Weight + Centripetal Force = 735 N + 120 N = 855 N.
So, Tarzan exerts a total force of 855 Newtons on the vine.