A, B, C and D are four points on a hemispherical cup placed inverted on the ground. Diameter BC = 360 cm and AE = R/3 (R is the radius of the cup). A small spherical mass 500 g at rest at the point A, slides down along the smooth surface of the cup. Assuming that there is no loss of energy, calculate its:
(a) Potential Energy at A relative to B.
(b) Speed at the point B (lowest point).
(c) Kinetic Energy at D (g = 10 m s^-2).

Question

A, B, C and D are four points on a hemispherical cup placed inverted on the ground. Diameter BC = 360 cm and AE = R/3 (R is the radius of the cup). A small spherical mass 500 g at rest at the point A, slides down along the smooth surface of the cup. Assuming that there is no loss of energy, calculate its:
(a) Potential Energy at A relative to B.
(b) Speed at the point B (lowest point).
(c) Kinetic Energy at D (g = 10 m s^-2).

KnowledgeBoat · Accepted Answer

Given, - Diameter (2R) = 360 cm = 3.6 m - Radius (R) = 1.8 m - Mass of the sphere (m) = 500 g = 0.5 kg - AE = = 0.6 m - Acceleration due to gravity (g) = 10 m s-2 Condition : No energy loss so energy is conserved. (a) As, point B is on the ground then Height of point A relative to point B = radius of hemisphere (R) = 1.8 m Potential energy UA at A relative to B is given by UA = m x g x R Substituting the values we get, UA = 0.5 x 10 x 1.8 ⇒ UA = 9 J Hence, the potential energy at point A relative to point B is 9 J. (b) As there are no energy losses so total mechanical energy is same at all points of the path due to conservation of mechanical energy and all the potential energy at point A will be converted to kinetic energy at point B. Let, speed at point B be 'vB'. Then, Kinetic energy at B = UA So, speed at point B is 6 m s-1. (c) As points D and E are on the same height so at these points their potential and kinetic energies are equal i.e., Potential energy at point D = Potential energy at point E And Kinetic energy at point D = Kinetic energy at point E Now, Distance of point D from the ground = R - AE = 1.8 - 0.6 = 1.2 m Thus, potential energy at point D = mg x 1.2 = 0.5 x 10 x 1.2 = 6 J Mechanical energy at point D = Potential energy at point D + Kinetic energy at point D As, mechanical energy is conserved, Mechanical energy at point D = Potential energy at point A ⇒ Potential energy at point D + Kinetic energy at point D = 9 ⇒ 6 + Kinetic energy at point D = 9 ⇒ Kinetic energy at point D = 9 - 6 = 3 J So, kinetic energy at point D is 3 J.

Physics

Work, Energy & Power

Related Questions

A metal rod AB of length 80 cm is balanced at 45 cm from the end A with 100 gf weights suspended from the two ends.
(a) If this rod is cut at the centre C, then compare the weight of AC to the weight of BC.
(b) Give a reason for your answer in (a)

For each of the following scenarios, state whether the work done by gravity is positive, negative, or zero.
(a) a person walks on a levelled road.
(b) a person climbs a ladder.
(c) a car in neutral gear is coming down the slope.

A block and tackle system of pulleys has velocity ratio 4.
(a) Draw a labelled diagram of the system indicating clearly, the direction of the load and effort.
(b) Calculate the potential energy of the load 100 kgf lifted by this pulley to a height 5 m. (g = 10 ms^-2)

Physics

Work, Energy & Power

Related Questions

A metal rod AB of length 80 cm is balanced at 45 cm from the end A with 100 gf weights suspended from the two ends.(a) If this rod is cut at the centre C, then compare the weight of AC to the weight of BC.(b) Give a reason for your answer in (a)

For each of the following scenarios, state whether the work done by gravity is positive, negative, or zero.(a) a person walks on a levelled road.(b) a person climbs a ladder.(c) a car in neutral gear is coming down the slope.

A block and tackle system of pulleys has velocity ratio 4.(a) Draw a labelled diagram of the system indicating clearly, the direction of the load and effort.(b) Calculate the potential energy of the load 100 kgf lifted by this pulley to a height 5 m. (g = 10 ms-2)

A metal rod AB of length 80 cm is balanced at 45 cm from the end A with 100 gf weights suspended from the two ends.
(a) If this rod is cut at the centre C, then compare the weight of AC to the weight of BC.
(b) Give a reason for your answer in (a)

For each of the following scenarios, state whether the work done by gravity is positive, negative, or zero.
(a) a person walks on a levelled road.
(b) a person climbs a ladder.
(c) a car in neutral gear is coming down the slope.

A block and tackle system of pulleys has velocity ratio 4.
(a) Draw a labelled diagram of the system indicating clearly, the direction of the load and effort.
(b) Calculate the potential energy of the load 100 kgf lifted by this pulley to a height 5 m. (g = 10 ms^-2)