Work Energy Theorem: THIS Question can be Done in 10 s

Question : A block of ice slides down a frictionless ramp at an angle θ = 50°, while an ice worker pulls on the block with a rope with a force Fr that has a magnitude of 50 N and is directed up the ramp.
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As the block slides through a distance d = 0.50 m along the ramp, its kinetic energy increases by 80 J. How much greater would its kinetic energy have been if the rope had not been attached to the block? That is, for the same displacement of 0.5 m, how much more KE would it have gathered if this upward force was not present?
Solution
This question, though it looks complicated, can be quite straightforward for those familiar with the concepts. Some students might solve it quickly, while others might take a bit longer, but both approaches are valuable.
The long approach involves understanding the work-energy theorem, which states that the change in kinetic energy is equal to the total work done by all the forces.
In this problem:
Case 1: With the rope attached
ΔKE = Wg + Wr (A)
work done by gravity = Wg
work done by the rope = Wr
Wr = (Fr) (d) cos(180°) = (50 N) (0.5 m) (-1) = -25 J
(negative since the force and displacement are in opposite directions).
Given: ΔKE = 80 J, we can write (A) as-
80 J = Wg - 25 J
Wg = 80 J + 25 J = 105 J (1)
Case 2: Without the rope
The work done by gravity (Wg) remains the same.
There is no work done by the rope.
Equation (A) becomes
ΔKE(case 2) = Wg + 0 (2)
Then subtracting (1) from (2) gives
ΔKE(case 2) - 80 J = 25J or
ΔKE(case 2) = 105J
That means the extra KE generated would have been 105 J - 80 J = 25 J
If you have practiced similar problems, you would quickly recognize that the key is to determine the contribution of the work done by the rope to the kinetic energy (KE) change. In this scenario, the work done by the rope is -25 J. The negative sign indicates that the force exerted by the rope is reducing the kinetic energy. Therefore, if the force from the rope had not been present, the kinetic energy would have increased by this amount. Consequently, without the rope, the kinetic energy of the block would have increased by an additional 25 joules..
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Who is this for: Class 11 physics student, AP Physics students, students appearing for competitive exams like IIT JEE and NEET.
If you are an AP Physics C review student, or if you're looking for Class 11 physics notes PDF downloads on the topic of work energy and power you should visit our website. You can find quiz and pdf summary of the topic. Discover more work energy theorem and numerical problems that is widely used by students preparing for IIT JEE, NEET or IB Physics
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