Cheenta
How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances?
Learn More

Maximum Height of Object over a Pulley

Try this problem, useful for Physics Olympiad based on Maximum Height of Object over a Pulley.

The Problem: Maximum Height of Object over a Pulley

Two objects with masses 5Kg and 2Kg hang 0.6m above the floor from the ends of a cord 6m long passing over a frictionless pulley. Both objects start from rest. Find the maximum height reached by the 2.00Kg object.

Maximum Height of Object over a Pulley

Diagram of the pulley

Discussion:

Set up : After the (5Kg) object reaches the floor, the (2Kg) object is in free fall, with downward acceleration (g).

Execution: The (2Kg) will accelerate upward at$$ \frac{5-2}{5+2}g=3g/7$$ and the (5Kg) object will accelerate downward at (3g/7).

Let the initial height above the ground be (h_0).

When the large object hits the ground, the small object will be at a height (2h_0) and moving upward with a speed given by $$ v_0^2=2ah_0=6gh_0/7$$. The small object will rise to a distance (v_0^2/2g=3h_0/g) and so the maximum height reached will be $$ 2h_0+3h_0/7=17h_0/7=1.46m$$ above the floor, which is (0.860m) above its initial height.

Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy
Cheenta

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com