A sphere of mass 85 kg is attached to one end of a rope as shown in the figure below. It is found that the rope does an amount of work
W = 8030 J
in pulling the sphere upward through a distance 9.6 m. Find the tension in the rope.
assumeing the mass is stopped at the end of the pull.
force*distance=work
solve for force.
I think it is 8030/9.6 = 836.453333
Backsolving: 836.4583333*9.6 = 8030
Force is 836.4583333
To find the tension in the rope, we can use the work-energy theorem. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.
In this case, the sphere is being pulled upward against the force of gravity, so the work done by the rope is equal to the change in potential energy of the sphere.
The equation for the work done on the sphere is:
W = ΔPE (change in potential energy)
The potential energy of an object near the surface of the Earth is given by:
PE = mgh
where m is the mass of the object, g is the acceleration due to gravity, and h is the height.
In this case, the sphere is being pulled upward through a distance of 9.6 m, so the change in potential energy (ΔPE) is given by:
ΔPE = mgh
Plugging in the given values, we have:
ΔPE = (85 kg)(9.8 m/s²)(9.6 m)
Now, since the work done is equal to the change in potential energy, we can equate the two:
W = ΔPE
8030 J = (85 kg)(9.8 m/s²)(9.6 m)
Simplifying the equation, we find:
Tension (in the rope) = W / distance
Tension = 8030 J / 9.6 m
Evaluating the expression, we get:
Tension ≈ 835.42 N
Therefore, the tension in the rope is approximately 835.42 Newtons.