* Force = mass x acceleration
* F = ma
* Weight of a body= mass of the body x acceleration due to gravity.
* W= mg
* Moment of force = force x perpendicular distance
-- Principle of moments
* Total clockwise moments= total anticlockwise moments.
* Work = force x displacement
* W = F x d
* K. E= 1/2 mv²
* P. E= mgh
* Power= work/time.
EXERCISE --1
1) a man of mass 60 kg runs up a flight of 30 stapes in 15 seconds. If each step is 20 cm high, calculate the power developed by the man (g=10/sec²). 240 W
2) A bullet of mass 50gm is moving with a velocity of 500m/sec. It penetrates 10cm. into target and comes to rest.
A) Calculate the kinetic energy possessed by Bullet. 6250J
B) average retarding force offered by target. 62500N
3) A vehicle moves with velocity of 36 km/hr. A force of 2000 N acts on it. Calculate the power of vehicle. 20000 W
4) A force of 200 dynes acts on a mass of 0.04kg over a distance of 10m. Assuming mass initially at rest, find its final velocity and time for which force acts. 20sec
5) A cricket ball weighing 150gm rises to a vertical height of 6m and drops vertically into the hands of a fielder when 1.1m above the ground. The fielder brings it to rest in 1/10sec. Calculate
A) speed of the ball as it reaches the fielders hands. 9.8 m/sec
B) The force applied by fielder's hands to the ball during the process of stopping it. 14.7 N
6) A hockey ball, at rest, is hit by a hockey stick such that the force acts on the ball for 0.15sec. If the ball is of mass100gm and covers a distance of 100m in 2 second, find the magnitude of force. (assume there is no force of friction). 33.33 N
7) A cricket ball moving with a velocity of 35 m/sec is a brought to rest by a player in 0.4 seconds. If the mass of the ball is 0.105 kg, find
A) impulse . - 3.675 NS
B) average retarding force applied by a player. -9.19 N
8) A spaceship weighs 2000 kg. Its engine fires for 20 second. If the initial velocity of rocket is 20 km/sec and thrust developed by its engine is 100000 N, find the final velocity of spaceship and distance covered by it. 41km/hr, 810 km.
9) How much work will have to be done by a body on a ball of mass 50gm to give it a momentum of 500gm. ACM/sec. 2.5 x 10⁴ J
10) A boy weighing 350 N runs up a flight of 30 stapes, each 20 cm high, in 5 second. calculate the power expanded. 420 watt.
11) A boy of mass 40 kg runs upstairs and reaches the 8 metre heigh 1st floor in 5 sec. Calculate
A) force of gravity acting on the boy . 400 N
B) work done by him against gravity. 3200J
C) the power developed by the boy (g= 10m/sec). 640 watt
12) A water pump raises 50kg of water through a height of 25m in 5 second. Calculate the power which the pump supplies (g= 10m/s²). 2500 watt.
13) A truck weighing 1000 kg changes its speed from 36km/hr to 72km/hr in 2 minutes. Calculate the work done by engine and its power. (H. P=746 watt).
14) Two bodies of equal masses are kept at a height h and 2h, respectively. What is the ratio of their potential energies? 1/2.
15) A body of mass 1 kg. falls from a height 5 metre. How much energy does it process at any instant ? (g= 9.8 m/sec²).
16) Find the kinetic energy of a body of mass 1 kg moving with a uniform velocity of 10m/sec. 50J
17) Find potential energy of mass 1 kg is kept at a height of 5 metre, if g= 10 m/sec³. 50J
18) A body of mass 60 kg has momentum 3000kg/sec. calculate kinetic energy and speed of body. 7.5x 10⁴J
19) A stone 500gm is thrown vertically upward with a velocity of 15m/sec. Calculate
A) potential energy. 56.25J
B) kinetic energy on reaching ground. 56.25 J
20) Calculate the work done by a man (mass 50 kg) and hence increase in his potential energy. when he climbs up a ladder 10m high.(g= 9.8 m/sec²). 4900J
21) A ball of mass 0.5 kg slows down from speed of 5 m/sec to that of 3m/sec. Calculate the change in kinetic energy of ball. 4J
22) How fast should a man weighing 60 kg. run to that kinetic energy is 750J? 5m/sec
23) A body of mass 50 kg runs a flight of 100 stairs in 20 seconds. if each stair is 25 cm high and value of g is 10m/sec², find
A) gravitational force acting on a body. 500N
B) work done by the boy. 12500J
C) gain in potential energy. 12500J
D) power of the body in watts. 625 watt.
24) An object of mass 2.0 kg is lifted vertically through a distance of 1.5 metre. What is the work done ? (g=9.8m/sec²). 29.4 J
25) A force of 50N is used to push a body on a frictionless table. The body continues to move according to Newton's first law of motion. Calculate the work done by force.
26) A boy weighing 50kg climbs up a vertical height of 10 metre. Calculate the amount of work done(g= 9.8 m/sec²). 4900J
27) Calculate the work done by a passenger on a platform holding a suitcase of 20 kg.
28) Calculate the work done by a passenger on a platform carrying a box of 30 kg. 0
29) What is the kinetic energy of a ball of mass 0.1 kg, when it is thrown with a speed of 15m/sec? 11.25J
30) The mass of a car is 12 kg. Calculate its kinetic energy when it is moving with a speed of 80 km/h. 80000/27 J
31) A bullet of mass 10gm is fired with a velocity of 80m/sec. Calculate its kinetic energy in joules. 32J
32) How fast should a man of mass 50 kg run so that his kinetic energy is 625 J? 5m/sec
33) Two bodies of equal mass move with the velocity of 2v and 3v, respectively. What is the ratio of their kinetic energies? 4:9
34) A man drops a 10kg rock from the top of a 5m ladder. What is its kinetic energy. when it reaches the ground? what is its speed just before it hits the ground?(g=9.9 m/sec²). 9.9m/sec
35) A body of mass 2 kg is dropped from the top of a tower of height 100m. If the acceleration, due to gravity is 10m/sec², calculate its kinetic energy at the end of 5 sec. 2500 J
36) A car weighing 1000 kg and traveling at 30 m/sec stops at a distance of 50m deaccelerating uniformly. What is the force exerted on it by the brakes ? what is the work done by the brakes? 9000N, 450000J
37) A man of 50 kg jumps a height of 1.2m. What is the potential energy at the height point?(g=10m/sec²). 600J
38) A block of 20 kg mass is pulled up a slope by applying a force acting parallel to the slope and it makes an angle of 30° with the horizontal. Calculate the work done in pulling the block up a distance of 3m. What is the increase in potential energy of block ? 300J
39) A bullet of mass 60gm moving with a velocity of 360m/sec gets embedded in a freely suspended wooden block of 600gm. What is the velocity acquired by the block ? 108.54 m/sec
40) A man of mass 60 kg runs up a flight of 30 steps in 40 seconds. If each steps is 20cm high, calculate his power. 90W.
41) The engine of a train has to apply a force of 5000N to overcome friction to run at a uniform rate of 90 km/hr. What is the power developed by engine? 125 kW.
42) What is escape velocity ?
43) A bullet of mass 5gm travelling at a speed of 120 m/sec penetrates deeply into a fixed target and is brought to rest in 0.01 seconds. Calculate
A) the distance of penetration in the target . 0.06m
B) the average force exerted in the bullet . 60N
44) What is the weight of an object of mass 20 kg on Earth? What will be its weight and mass on the moon? value of g on moon is 1.6 m/sec²and on Earth is 9.8 m/sec². 32N
45) What force and what weight act on a mass of 10.5 kg being pulled by Earth? g=10m/sec². 105N
46) A force of 10N displaces a body by a distance of 2 metre at an angle 60° to its own direction. Find the amount of work done. 10J
47) Calculate the power of an engine required to life 10⁵ kg of coal per hour from a mine 360m deep (g= 10m/sec²). 10⁵w
48) An electric motor power 100W is used to drive the stirrer in a water boat. If 50% of the energy supplied to the motor is spent is stirring the water. Calculate the work done on the water in 1 minute. 3000J
49) A pump is to life 500kg of water from a depth of 80m in 10 seconds. Calculate
A) work done by pump. 4x10⁵J
B) power rating of pump if its efficiency is 40%. 100 Ke.
50) A mass of 5.25 kg is being pulled by the earth. What force and what weight will acting on it. g= 10m/sec². 5.25 khet
51) A body of mass 1 kg falls from a height of 5 metre. how much energy does it possess at any instant? g=10m/sec². 49J
52) In a damn, generating Hydro electric power water falls at a rate of 1000kg/sec. from a height of 100 m
A) calculate the initial potential energy of water. 9.8x 10⁵J
B) Assuming that 60% of energy of falling water is converted to the electrical energy. Calculate the power generated (g= 102 sec²). 5.88x 10⁵W
EXERCISE--2
1) if one wishes to accelerate a 1000 kg mass from 5m/sec to 10 m/sec in 58 second, what would be required ? 1000N
2) what is the acceleration produced by a force 20N exerted on an object of 4 kg mass? 0.5 m/sec²
3) To produce an acceleration of 10m/sec² on a bowling ball with a mass of 5 kg, what force would be required ? 50N
4) compute the acceleration produced when a force of 50 N acts on a body of mass 25 kg. 2m/sec²
5) what is the magnitude of the force which produces an acceleration of 1 m/sec² in a body of mass 1 kg ? 1 N
6) A force of 100N produces an acceleration at 25m/sec² to a body. what is the mass of the body? 4 kg
7) A force F acting on a body of mass m produces an acceleration of 'a' in it. The same force when acts on another body produces an acceleration of 3a in it. What is the mass of the second body ? m/3
8) A force of 20N acts for 5 seconds on a mass of 4 kg. Calculate the change in velocity of the mass. 25 m/sec
9) A force of 25N acts for 4 second on a body of mass 2 kg virtually at rest. Determine
A) the acceleration produced. 12.5 m/sec²
B) the velocity of the body at the end of 4 second. 50 m/sec
C) the distance moved by during the time. 100 cm
10) A steel ball of mass 10 gram hits a hard surface vertically with a speed of 5m/sec and rebounds with the same speed. The ball remains in contact with surface for 1/100 second. Calculate the average force exerted by surface on the ball. 10N
11) A force acts for 10 seconds on a body of mass 10gm, after which the force ceases to act. The body travels a distance of 50cm in next 4 second. what is the magnitude of the applied force. 1/10⁴ N
12) A force of 100N moves a body to a distance of 50cm. Calculate the work done by force. 50J
13) Find the work done by a force that moves of mass 2kg through a distance of 5m with a constant acceleration of 0.4 m/sec².
14) A bullet of mass 20g is moving with a constant velocity of 200m/sec. what is its kinetic energy . 400J
15) A body of mass 10 kg is dropped from a height of 20m. Find
A) potential energy. 1960J
B) its kinetic energy when 8 metre above the ground. 1176J
C) its kinetic energy when it reaches the ground. 1960J
16) A man of mass 60 kg carrying a load of 15 kg on his head, walks up 15 steps each 20cm high in 5 second. find the power he developed. 294 watts
17) A man of mass 60 kg climbs a ladder 5 metre long that makes an angle of 45°C with horizontal ground. Calculate the work done by him against gravity. 2940J
18) Compute the work done by a man weighing 60 kgf in carrying a load of 40 kgf at his back through a distance of 10 metre
A) in vertical direction. 10000J
B) in horizontal direction up a smooth inclined plane which rises 1 in 100 i.e., sin x°= 1/100. 1000J
19) Calculate the work done by a 5 kW metre in 30 minutes. 9x10⁶J
20) Calculate the power of a pump which can lift 200 kg of water to a water tank at a height of 50 metre in 20 second. g= 10 m/sec².
21) A man weighing 65 kgf lifts a mass of 35 kg to s height of 10m in 40 sec. computer his power. 250W.
22) A truck weighing 50x10³kg and a cart weighing 500 kg are moving with same speed. compute their kinetic energies. 100: 1
23) Calculate the kinetic energy of a body of mass 0.10 kg and Momentum 20 kg m/sec. 2x10³J
24) find out
A) kinetic energy 4x 10⁵J
B) the momentum of a car of mass 2000 kg is travelling at 72 km/hr. 4x 10⁴ kg m/sec
25) A car is travelling with a velocity of 54 km/hr. If the car weighs 9800N, what force is required to stop the car in 100m distance (g= 9.8 m/sec²). 1125N
26) A 2kg ball vertically at rest at a height of 5 metre above the ground level, is allowed to drop freely calculate
A) the potential energy possessed by the ball when initially at rest,. 100J
B) kinetic energy of ball before it hits the ground. 100J
27) A body of mass 60 kg has momentum of 3000 kg m/sec. calculate
S) speed of body. 50 m/sec
B) the K. E of the body. 75000J
28) calculate the mass of a body which is moving with a velocity of 50 m/sec and has a K. E of 200J. 0.16 kg
29) A man weighing 70 kgf carries a load of 10 kg to the top of a tower 100m high. Find the amount of work done (g= 9.8 m/sec²). 78400J
30) How much work is done by earth's gravitational field on a trunk weighing 60N when you carry the trunk down to a basement 3 metre below the ground floor. 280J
31) In a dam, generating hydro electric power, water falls at a rate of 1000 kg/sec from a height of 100m. assuming that 60% of the energy of falling water is converted to electrical energy, calculate the energy generated per sec (g= 9.8 m/sec²). 288000J
32) From the following table answer the following questions:
Time Distance (mm) cov
m(s) obj-A obj-B obj- C
--- ----- ------. ---------
1st 20 20 20
2nd 20 30 60
3rd 20 40 100
4th 20 25 140
5th 20 50 180
A) which object is moving with uniform velocity.
B) which object is moving with uniform acceleration? find out the acceleration.
C) which object is moving with irregular acceleration ?
D) find the distance covered by each object in 5 seconds.
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