A sphere of mass 78 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 = 3550 J
in pulling the sphere upward through a distance 4.6 m. Find the work done by the force of gravity on the sphere.
My work
W= -78 * 9.8 * 4.6 = -3516.24
Answer: -3520
To find the work done by the force of gravity on the sphere, we can use the formula:
Work = Force * Distance * cos(theta)
Since the sphere is being pulled upward, the force of gravity is opposing the motion, so the angle theta between the force of gravity and the direction of motion is 180 degrees.
Let's calculate the work done by the rope first:
W = 3550 J
Now, we can use the equation to find the force applied by the rope:
Force = Work / (Distance * cos(theta))
= 3550 J / (4.6 m * cos(180 degrees))
Since cos(180 degrees) = -1, we can simplify the equation:
Force = -3550 J / (4.6 m)
Next, we can calculate the work done by the force of gravity:
Work_gravity = Force_gravity * Distance * cos(theta)
The force of gravity on the sphere is given by:
Force_gravity = Mass * Acceleration_due_to_gravity
= Mass * g
Here, the mass of the sphere is given as 78 kg, and the acceleration due to gravity is approximately 9.8 m/s^2.
Substituting the values:
Force_gravity = 78 kg * 9.8 m/s^2
Now, we can calculate the work done by the force of gravity:
Work_gravity = (78 kg * 9.8 m/s^2) * 4.6 m * cos(180 degrees)
Since cos(180 degrees) = -1, we can simplify the equation:
Work_gravity = (78 kg * 9.8 m/s^2) * 4.6 m * (-1)
Calculating:
Work_gravity = -3516.24 J
Therefore, the work done by the force of gravity on the sphere is approximately -3516.24 J.