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In this lesson, we will learn how to apply the conservation of energy principle to solve problems on moving bodies.

Q1:

A body started to slide down a smooth inclined plane of height 504 cm from its top. Find its speed when it reached the bottom. Take π = 9 . 8 / m s 2 .

Q2:

A body of mass 840 g was placed at the top of a plane inclined to the horizontal at an angle whose tangent is 4 3 . It was released from rest and slid freely down the plane. When it reached the bottom of the plane, its speed was 1 m/s. Given that the change in the bodyβs gravitational potential energy was 1.68 joules, determine the resistance of the plane to the motion of the body. Consider the acceleration due to gravity to be 9.8 m/s^{2}.

Q3:

A body of mass 4 kg fell vertically from a height of 28 m above the surface of the ground. Find its gravitational potential energy π relative to the ground and its kinetic energy π when it was 7 m above the ground. Consider the acceleration due to gravity to be 9.8 m/s^{2}.

Q4:

A body started sliding down the line of greatest slope of a smooth inclined plane. When it was at the top of the plane, its gravitational potential energy relative to the bottom of the plane was 1β830.51 joules. When it reached the bottom of the plane, its speed was 8.6 m/s. Find the mass of the body.

Q5:

A body of mass 80 g was projected upwards from the ground. The sum of its kinetic energy and its gravitational potential energy relative to the ground is constant along its path and is equal to 22β688 g-wtβ cm. Find the speed of the body when it was at a height of 2.8 m above the ground. Consider the acceleration due to gravity to be π = 9 . 8 / m s 2 .

Q6:

A body of mass 7 kg fell vertically from point π΄ to the ground. Given that, when it reached the ground, its kinetic energy was 3β724 joules, find its gravitational potential energy relative to the ground when it was at point π΄ . Consider the acceleration due to gravity to be 9.8 m/s^{2}.

Q7:

A projectile was fired vertically upwards from the Earthβs surface at 1β218 m/s. It hit a target that was 1β575 m above the surface of the Earth. Find the speed of the projectile when it hit the target. Consider the acceleration due to gravity to be 9.8 m/s^{2}.

Q8:

A body was projected from a point π΄ up the line of greatest slope of a smooth plane inclined at 3 0 β to the horizontal. It took 6 seconds to reach point π΅ at which its kinetic energy was 3.6 kg-wtβ m. The work done by the body in moving from π΄ to π΅ was β 1 3 . 3 kg-wtβ m. Using the work-energy principle, find the speed π£ 1 of the body at π΄ and the speed π£ 2 of the body at π΅ . Consider the acceleration due to gravity to be π = 9 . 8 / m s 2 .

Q9:

A body was projected up the line of greatest slope of a rough plane inclined at an angle π to the horizontal from its bottom. When it came to rest at a height of 90 cm, its change in potential energy was 83.7 joules. The body slid back down the slope. When it reached the bottom, its kinetic energy was 30.6 joules. Given that the resistance to the bodyβs motion was 6 N throughout its movement, determine the initial kinetic energy of the body π , and find the sine of the angle of inclination of the plane, s i n π .

Q10:

A body of mass 20 kg fell from a height of 42.3 m above the surface of the ground. Find the sum of its kinetic energy and its potential energy relative to the ground 2 seconds after it started falling. Take π = 9 . 8 / m s 2 .

Q11:

A particle of mass 281 g was projected at 37 cm/s up the line of greatest slope of a smooth plane inclined to the horizontal at an angle whose sine is 1 0 1 1 . Determine the change in the particleβs gravitational potential energy from the moment it was projected until its speed became 29 cm/s.

Q12:

An airport baggage delivery slide is constructed from two smooth arcs, π π and π π as shown in the diagram. π π is an arc on a circle with radius 3 m, subtending an angle of 2 5 β at its centre π΄ . π π is an arc on a circle with radius 5 m, subtending an angle of 3 8 β at its centre π΅ . Points π and π΅ are directly below π΄ . The bags land on a conveyer belt 0.9 m below π . To test the chute, a small particle is released from rest at π . Assuming that the particle will reach π , find the speed with which the particle hits the conveyor belt. Consider gravitational acceleration to be π = 9 . 8 / m s 2 and give your answer correct to one decimal place.

Q13:

A sphere started moving down a rough inclined plane of length 50 m. When it reached the bottom of the plane, it had descended 15 m vertically and it continued moving along a horizontal plane of the same resistance. Given that 1 7 of the gravitational potential energy was lost as a result of the work done against the resistance of the plane, find the speed π£ of the sphere at the bottom of the inclined plane and the distance π covered by the sphere along the horizontal plane. Consider the acceleration due to gravity to be 9.8 m/s^{2}.

Q14:

A body was projected up the line of greatest slope of a smooth plane inclined at 3 0 β to the horizontal. After moving for 6 seconds, its kinetic energy was 2.42 kg-wtβ m. Given that the work done by the body in this time was β 1 8 . 0 6 kg-wtβ m, use the work-energy principle to find the mass of the body. Take π = 9 . 8 / m s 2 .

Q15:

A body was projected up a rough inclined plane from its bottom. Its initial kinetic energy was 242 joules. The body continued moving until it reached its maximum height and then slid back down to the bottom. When it reached the bottom, its kinetic energy was 186 joules. Find the work done against friction π during the ascent and the gain in gravitational potential energy π when the body was at its maximum height.

Q16:

A simple pendulum, consisting of a light string of length 44 cm with a mass of 82 grams attached to its end, swings through an angle of 1 2 0 β . Determine the speed of the mass at the lowest point of its swing. Consider the acceleration due to gravity to be 9.8 m/s^{2}.

Q17:

A simple pendulum, consisting of a light string of length 36 cm with a mass of 65 grams attached to its end, swings through an angle of 1 2 0 β . Determine the speed of the mass at the lowest point of its swing. Consider the acceleration due to gravity to be 9.8 m/s^{2}.

Q18:

A body of mass 9 kg fell vertically from a point 3.4 m above the ground. At a certain moment, the speed of the body was 3.9 m/s. Determine the change in the bodyβs gravitational potential energy from this point until it reached a point 68 cm above the ground. Take π = 9 . 8 / m s 2 .

Q19:

A simple pendulum, consisting of a light string of length 32 cm with a mass of 14 g attached to its end, swings through an angle of 1 2 0 β . Find the increase in its gravitational potential energy as it moves from its lowest point to its highest point. Take π = 9 . 8 / m s 2 .

Q20:

The figure shows a body of mass 1 4 kg before it started to slide along the surface. The two surfaces π΄ π΅ and πΆ π· are smooth. However, the horizontal plane π΅ πΆ is rough, and its coefficient of kinetic friction is 7 1 0 . If the body started moving from rest, find the distance that the body covered on π΅ πΆ until it came to rest. Consider the acceleration due to gravity to be π = 9 . 8 / m s 2 .

Q21:

A body of mass 55 g started sliding down a smooth inclined plane. Find the gravitational potential energy lost by the time the bodyβs speed reached 2 m/s.

Q22:

A car descended 195 m on a slope from rest, which is equivalent to a vertical distance of 14 m. Given that 2 7 of the potential energy was lost due to resistance and that the resistance remained constant during the carβs motion, determine the carβs velocity after it had travelled the mentioned distance of 195 m. Take π = 9 . 8 / m s 2 .

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