A massless string runs around two massless, frictionless pulleys, where one pulley is attached to the ceiling, and the other is suspended with a mass m. An object with mass m = 17 kg hangs from one pulley. A force F is exerted on the free end of the string to lift the object at a constant speed by a distance of 2.9 m. What is the work done on the object by the force F? Hint: Use the lower pulley and the attached object as the system and note that the force F is the tension in the string.
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17KG (mass hanging from pulley)
F is external force pulling the string that runs over the pulley. * is a pulley one attached to the ceiling the other hanging. object of mass m=17kg hanging from string.
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Ok the above diagram didn't turn out the way i expected it to. But I hope you can still understand with the description. Please help, I tried it two times but I am not getting the correct answer.
To find the work done on the object by the force F, we need to calculate the force multiplied by the distance over which it acts. In this case, the force F is the tension in the string.
Let's break down the problem step by step:
1. Identify the system: The problem suggests using the lower pulley and the attached object as the system. This means we will consider the object and the pulley together as our system.
2. Determine the force acting on the system: The only external force acting on the system is the force F exerted on the free end of the string to lift the object. This force is the tension in the string.
3. Find the value of the force: The tension in the string is equal throughout the string. Since the object is in equilibrium (constant speed), the tension in the string is equal to the weight of the object (mg), where m is the mass of the object (17 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Tension (F) = weight of the object = mg = 17 kg * 9.8 m/s^2 = 166.6 N
4. Calculate the work done on the object: The work done on an object is given by force multiplied by distance: Work = Force * Distance.
In this problem, the force remains constant throughout the lifting process, and the object is lifted a distance of 2.9 m.
Work = Force * Distance = 166.6 N * 2.9 m = 482.14 Joules
Therefore, the work done on the object by the force F is 482.14 Joules.
To find the work done on the object by the force F, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
In this case, since the object is lifted at a constant speed, its kinetic energy remains constant. Therefore, the work done on the object is equal to zero.
The reason for this is that when an object is lifted at a constant speed, the force applied on it (in this case, the tension in the string) balances the force of gravity. As a result, the net work done on the object is zero, since there is no change in its kinetic energy.
So, the work done on the object by the force F is zero.