During a theatre refit, a scenery platform is raised from below the stage by two vertical steel cables. Fig. 1 shows the platform at one point in its journe...
Question 1 Report
During a theatre refit, a scenery platform is raised from below the stage by two vertical steel cables. Fig. 1 shows the platform at one point in its journey. The load, including lamps and a sound system, has a mass of 780 kg. It rises through 12 m at a constant velocity. The stage manager records the time as 15 s. Take gravitational field strength, g, as 10 N/kg. The cables are identical and share the load equally. Students are asked to use the figure to consider forces and energy in the lifting system.
(a) Calculate the weight of the platform and its load. [2]
(b) Calculate the tension in one cable. [2]
(c) Calculate the gain in gravitational potential energy of the load. [3]
(d) Calculate the useful power supplied in raising the load. [2]
(e) Explain why the upward force from both cables equals the weight while the platform travels at constant velocity. [2]
Answer Details
(a)
\[W=mg=780\text{ kg}\times10\text{ N/kg}=7800\text{ N}\]
The weight is 7800 N. [2]
(b) At constant velocity, total upward force equals weight, so the two cables together provide 7800 N. They share this equally:
\[\frac{7800\text{ N}}{2}=3900\text{ N}\]
The tension in one cable is 3900 N. [2]
(c)
\[\Delta E=mgh=780\text{ kg}\times10\text{ N/kg}\times12\text{ m}=93600\text{ J}\]
The gain in gravitational potential energy is 93 600 J. [3]
(d)
\[P=\frac{E}{t}=\frac{93600\text{ J}}{15\text{ s}}=6240\text{ W}\]
The useful power is 6240 W. [2]
(e) Constant velocity means zero acceleration. Therefore the resultant force is zero, so the total upward tension from both cables equals the downward weight. [2]
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