Law of Conservation of Mechanical Energy

Q. Use the following diagram to answer the question. Neglect the affect of resistance forces.

The object's kinetic energy at point C is less than its kinetic energy at point ____.

1. A only
2. D and E
3. A, D, and E
4. B only

Q. An archer pulls back 0.75 m on a bow which has a stiffness of 200 N/m. The arrow weighs 50 g. What is the velocity of the arrow immediately after release?

1. 48.9 m/s
2. 47.4 m/s
3. 50.0 m/s
4. 45.0 m/s

Q. A block of mass m initially at rest is dropped from a height h on to a spring of force constant k. the maximum compression in the spring is x then

1. 
2. 
3. 
4. 

Q. A particle falls from a height h upon a fixed horizontal plane and rebounds. If e is the coefficient of restitution, the total distance travelled before rebounding has stopped is

1. 
2. 
3. 
4. 

Q. Two identical cylindrical vessels with their bases at same level each contains a liquid of density ρ. The height of the liquid in one vessel is h₁ and that in the other vessel is $h_2$. The area of either base is A. The work done by gravity in equalizing the levels when the two vessels are connected, is

1. 
2. 
3. 
4. 

Q. Two identical blocks A and B, each of mass 'm' resting on smooth floor are connected by a light spring of natural length L and spring constant K, with the spring at its natural length. A third identical block 'C' (mass m) moving with a speed v along the line joining A and B collides with A. the maximum compression in the spring is

1. 
2. 
3. 
4. 

Q. A machine which is 75 percent efficient, uses 12 joules of energy in lifting up a 1 kg mass through a certain distance. The mass is then allowed to fall through that distance. The velocity at the end of its fall is (in m/s)

1. √32
2. √9
3. √18
4. √24

Q. A cyclist and his bicycle has a mass of 80 kg. After 100m he reaches the top of a hill, with slope 1 in 20 measured along the slope, at a speed of 2 m/s. He then free wheels the 100m to the bottom of the hill where his speed has increased to 9m/s. How much energy has he lost on the hill?

1. 844 J
2. 800 J
3. 837 J
4. 860 J

Q. A person on the street wants to throw an 8 kg book up to a person leaning out of a window 5 m above street level. With what velocity must the person throw the book so that it reaches the person in the window?

1. 5 m/s
2. 10 m/s
3. 8 m/s
4. 40 m/s

Q. A 0.5 kg block slides from the point A on a horizontal track with an initial speed 3 m/s towards a weightless horizontal spring of length 1 m and force constant 2 N/m. The part AB of the track is frictionless and the part BC has the coefficient of static and kinetic friction as 0.22 and 0.20 respectively. If the distance AB and BD are 2 m and 2.14 m respectively , then the total distance through which the block moves before it comes to rest completely is –[g = 10 m/s2].

1. 0.1 m
2. 0.2 m
3. 2.0 m
4. 1.0 m