In starting an exercise, a 1.60-m tall person lifts a 2.10 kg book from the the ground so it is 2.20m above the ground. What is the potential energy of the book relative to (a) the ground,and(b) the top of the persons head? (c) What is the work done by the person in part(a)?
To solve this problem, we can use the formulas for potential energy and work.
(a) To find the potential energy of the book relative to the ground, we can use the formula:
Potential Energy = mass * acceleration due to gravity * height
Given:
Height (h) = 2.20 m
Mass (m) = 2.10 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Potential Energy = 2.10 kg * 9.8 m/s^2 * 2.20 m
Potential Energy = 45.144 J
Therefore, the potential energy of the book relative to the ground is 45.144 J.
(b) To find the potential energy of the book relative to the top of the person's head, we need to consider the change in height.
The height difference between the book and the top of the person's head is the person's height, which is 1.60 m.
Potential Energy = mass * acceleration due to gravity * height
Height (h) = 2.20 m - 1.60 m = 0.60 m
Potential Energy = 2.10 kg * 9.8 m/s^2 * 0.60 m
Potential Energy = 11.628 J
Therefore, the potential energy of the book relative to the top of the person's head is 11.628 J.
(c) To find the work done by the person in part (a), we can use the formula:
Work = Force * Distance
The force applied by the person is equal to the weight of the book, which is given by the formula:
Force = mass * acceleration due to gravity
Force = 2.10 kg * 9.8 m/s^2
Force = 20.58 N
To calculate the distance, we can use the height difference, which is the same as part (b), 0.60 m.
Work = 20.58 N * 0.60 m
Work = 12.348 J
Therefore, the work done by the person in part (a) is 12.348 J.
To calculate the potential energy of an object, we need to use the formula:
Potential Energy = mass × acceleration due to gravity × height.
(a) To find the potential energy of the book relative to the ground, we'll use the height from the ground, which is 2.20 m.
Potential Energy (ground) = mass × gravity × height
= 2.10 kg × 9.8 m/s^2 × 2.20 m
= 45.816 J
Therefore, the potential energy of the book relative to the ground is 45.816 Joules.
(b) To find the potential energy of the book relative to the top of the person's head, we need to subtract the height of the person from the total height. The height of the person is 1.60 m, so the height from the top of the person's head becomes 2.20 m - 1.60 m = 0.60 m.
Potential Energy (head) = mass × gravity × height
= 2.10 kg × 9.8 m/s^2 × 0.60 m
= 12.276 J
Therefore, the potential energy of the book relative to the top of the person's head is 12.276 Joules.
(c) The work done by the person to lift the book from the ground can be calculated using the formula:
Work = force × distance
The force required to lift the book is equal to its weight, given by:
Force = mass × gravity
Work = Force × distance
= (2.10 kg × 9.8 m/s^2) × 2.20 m
= 45.816 J
Therefore, the work done by the person to lift the book from the ground is 45.816 Joules.
(a) From ground, h=2.30m so:
PE=mgh
=1.70kgx9.8m/sx2.30m
= 38.3J
(b)The person is shorter than the distance at which he holds the book from the ground so:
2.30-1.60=0.7m Use the same formula, just substitute 0.7 in for h.
(c)The work in this case is the potential energy of the book relative to ground, so it is equal to answer a.