The figure below shows Superhero hanging motionless from a rope, with Trusty Sidekick hanging below him. Superhero's mass is 89.0 kg, while Trusty Sidekick's is 58.0kg, and the mass of the rope is negligible.
(a) Find the tension in the rope at a point between Superhero and Trusty Sidekick.
N
(b) Find the tension in the rope at a point above Superhero.
N
To find the tension in the rope at different points, we need to consider the forces acting on each object.
(a) To find the tension in the rope at a point between Superhero and Trusty Sidekick, we can analyze the forces acting on Superhero. In this case, there are two forces acting on Superhero: his weight (mg) pulling him downward and the tension in the rope pulling him upward.
Since Superhero is motionless, the net force acting on him is zero. Therefore, the tension in the rope is equal to the weight of Superhero. The formula to calculate weight is:
Weight = mass * gravity
where mass is given as 89.0 kg and gravity is a constant value, typically taken as 9.8 m/s^2.
So, the tension in the rope between Superhero and Trusty Sidekick is:
Tension = Weight of Superhero = mass of Superhero * gravity
Tension = 89.0 kg * 9.8 m/s^2
Tension ≈ 872 N
Therefore, the tension in the rope at a point between Superhero and Trusty Sidekick is approximately 872 Newtons.
(b) To find the tension in the rope at a point above Superhero, we again need to consider the forces acting on Superhero. In this case, the tension in the rope is now pulling Superhero upward, against his weight.
To find the tension, we need to analyze the net force acting on Superhero. At equilibrium (motionless), the net force is zero. So, the tension in the rope above Superhero is equal to his weight.
Therefore, the tension in the rope above Superhero is the same as the tension between Superhero and Trusty Sidekick, which is approximately 872 Newtons.
To find the tension in the rope at different points, we can use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
(a) Finding the tension in the rope between Superhero and Trusty Sidekick:
Since both Superhero and Trusty Sidekick are hanging motionless, their accelerations are zero. Therefore, the net force acting on each of them must be zero.
Let's denote the tension in the rope between Superhero and Trusty Sidekick as T_shts.
For Superhero:
The only force acting on Superhero is the tension in the rope, T_shts. Since he is hanging motionless, the net force on him must be zero. Therefore:
T_shts - weight of Superhero = 0
The weight of Superhero can be calculated by multiplying his mass by the acceleration due to gravity, g, which is approximately 9.8 m/s^2.
Weight of Superhero = mass of Superhero * g
= 89.0 kg * 9.8 m/s^2
Using this, we can solve for T_shts.
(b) Finding the tension in the rope above Superhero:
Since Superhero is hanging motionless, the tension in the rope above him, which we'll denote as T_s, must be equal to his weight.
Let's calculate T_s using the weight of Superhero calculated in part (a).
T_s = weight of Superhero
= 89.0 kg * 9.8 m/s^2
So, the tension in the rope between Superhero and Trusty Sidekick (T_shts) is calculated in part (a), and the tension in the rope above Superhero (T_s) is calculated in part (b).