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In this lesson, we will learn how to find potential energy and the change in it and use it to solve different problems.

Q1:

A body of mass 4 kg had a gravitational potential energy of 2β136.4 joules relative to the ground. Determine its height. Consider the acceleration due to gravity to be 9 . 8 / m s 2 .

Q2:

A body of mass 3 kg had a gravitational potential energy of 1β528.8 joules relative to the ground. Determine its height. Consider the acceleration due to gravity to be 9 . 8 / m s 2 .

Q3:

A crane lifts a body of mass 132 kg to a height of 20 m. Find the increase in the bodyβs gravitational potential energy. Consider the acceleration due to gravity π = 9 . 8 / m s 2 .

Q4:

A crane lifts a body of mass 101 kg to a height of 6 m. Find the increase in the bodyβs gravitational potential energy. Consider the acceleration due to gravity π = 9 . 8 / m s 2 .

Q5:

A particle is moving from point ( 9 , 3 ) to point ( β 7 , 9 ) under the action of the conservative force β πΉ = β 1 0 β π β 7 β π dynes. Determine the change in the particleβs potential energy, given that the displacement is in centimetres.

Q6:

A particle is moving from point ( 8 , β 1 ) to point ( β 1 0 , β 3 ) under the action of the conservative force β πΉ = 6 β π β 3 β π dynes. Determine the change in the particleβs potential energy, given that the displacement is in centimetres.

Q7:

A body of mass 8 kg moved 238 cm up the line of greatest slope of a smooth plane inclined at 3 0 β to the horizontal. Calculate the increase in its gravitational potential energy. Take π = 9 . 8 / m s 2 .

Q8:

A body of mass 7.5 kg is at a height of 14 cm above the ground. Determine the potential energy of the body relative to the ground, take π = 9 . 8 / m s 2 .

Q9:

A body of mass 7 kg moved 52 cm up the line of greatest slope of a smooth plane inclined at 6 0 β to the horizontal. Find the increase in its gravitational potential energy. Take π = 9 . 8 / m s 2 .

Q10:

A body of mass 3 kg moved 120 cm up the line of greatest slope of a smooth plane inclined at 3 0 β to the horizontal. Find the increase in its gravitational potential energy. Take π = 9 . 8 / m s 2 .

Q11:

A body of mass 543 g is at a height of 22 m above the surface of the ground. Determine its gravitational potential energy relative to the ground, rounding your answer to two decimal places. Take π = 9 . 8 / m s 2 .

Q12:

A body of mass 580 g is at a height of 10 m above the surface of the ground. Determine its gravitational potential energy relative to the ground, rounding your answer to two decimal places. Take π = 9 . 8 / m s 2 .

Q13:

A helicopter of mass 3β830 kg descended vertically from a height of 370 m to a height of 280 m. Find its loss in gravitational potential energy. Consider the acceleration due to gravity to be .

Q14:

A helicopter of mass 2β630 kg descended vertically from a height of 250 m to a height of 150 m. Find its loss in gravitational potential energy. Consider the acceleration due to gravity to be .

Q15:

A ball of mass 317 g was projected vertically upwards at 29 m/s from a point π΄ . It passed through a point π΅ , at 21 m/s, where π΅ is vertically above π΄ . Neglecting air resistance, use the work-energy principle to find the increase in the ballβs gravitational potential energy as it moved from π΄ to π΅ .

Q16:

A ball of mass 334 g was projected vertically upwards at 22 m/s from a point π΄ . It passed through a point π΅ , at 18 m/s, where π΅ is vertically above π΄ . Neglecting air resistance, use the work-energy principle to find the increase in the ballβs gravitational potential energy as it moved from π΄ to π΅ .

Q17:

A body is moving in a straight line from point π΄ ( β 6 , 0 ) to point π΅ ( β 5 , 4 ) under the action of the force β πΉ = οΊ π β π + 2 β π ο N . Given that the change in the bodyβs potential energy is 2 joules and that the displacement is in metres, determine the value of the constant π .

Q18:

A body is moving in a straight line from point π΄ ( 5 , β 7 ) to point π΅ ( β 7 , 5 ) under the action of the force β πΉ = οΊ π β π + 4 β π ο N . Given that the change in the bodyβs potential energy is β 8 4 joules and that the displacement is in metres, determine the value of the constant π .

Q19:

A body is moving under the action of a constant force β πΉ = οΊ 5 β π + 3 β π ο N , where β π and β π are two perpendicular unit vectors. At time π‘ seconds, where π‘ β₯ 0 , the bodyβs position vector relative to a fixed point is given by β π = ο ( π‘ + 4 ) β π + ( 4 π‘ + 8 ) β π ο 2 2 m . Determine the change in the bodyβs potential energy in the first 9 seconds.

Q20:

A man of mass 92 kg is going from the sixth floor to the tenth floor in a lift. Given that the height of each floor is 3.3 m, determine the gain in gravitational potential energy. Consider the acceleration due to gravity to be 9.8 m/s^{2}.

Q21:

A person of mass 105 kg was hiking up a hill which was inclined to the horizontal at an angle whose sine is 1 3 . Given that he covered a distance of 87 m, find the change in his gravitational potential energy. Take π = 9 . 8 / m s 2 .

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