A solid sphere rolls down a roof

solid sphere rolls down a roofA solid sphere starts from rest and rolls without slipping a distance of 8 m down a roof that is inclined at 25˚. The roof’s edge is 5 m high from the ground. How far horizontally from the roof’s edge does the sphere hit the ground?

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A block is attached to a spring

block-spring-stone

A 15 kg block is firmly attached to a very light horizontal spring (k = 550 N/m) and resting on a smooth horizontal table. Suddenly it is struck horizontally by a 3 kg stone travelling with a velocity of 8 m/s to the right, whereupon the stone rebounds at 2 m/s to the left. Find the maximum distance that the block will compress the spring after the collision.

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A planet X around a star S

The diagram shows an approximate orbit of a planet X around a star S.

KeplerProblem

Which of the following statements is false?

(a) The planet moves in an ellipse with the star at one focus.
(b) The planet moves at the same speed at points A and C.
(c) The planet moves fastest at point D.
(d) The potential energy of the planet changes during the orbit.

 

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Human-Powered Helicopter

HPHA student builds a human-powered helicopter (HPH). It is a helicopter powered by one person carried on board and the power is generated by pedaling.
This human-powered helicopter has the following parameters: diameter of helicopter rotor blades is 15 meters and total mass is 100 kg. The air density 1.3 kg/m^3.

Can the HPH take off?

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Ring, Disc and Sphere

ringDiskSpher
A ring, a solid disc and a solid sphere are released simultaneously and roll down an inclined plane. What is the order of finish?

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Kinetic energy of the bicycle

sunsetmtbA bicycle has a kinetic energy of 100 J. What kinetic energy would the bicycle have if it had one half of the mass and was moving with twice the speed?

 
 
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Event violates the law of conservation …

carsCollisionThe two toy cars have equal masses. The cars move towards each other at 0.5 m/s. They collide and bounce off each other at 1 m/s. This event violates the law of conservation of
a) mass
b) momentum
c) kinetic energy
d) potential energy
e) (b) and (c)
f) charge
g) all of these  

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