High School

How much work is done in lifting a 1.2-kg book off the floor to put it on a desk that is 0.5 m high? Use the fact that the acceleration due to gravity is [tex]g = 9.8 \, \text{m/s}^2[/tex].

(b) How much work is done in lifting a 24-lb weight 4 ft off the ground?

**Solution:**

(a) The force exerted is equal and opposite to that exerted by gravity, so the force is [tex]mg = (1.2)(9.8)[/tex]. The work done is [tex]W = Fd = (1.2)(9.8)(0.5)[/tex].

(b) Here, the force is given as 24 lb. The work done is [tex]W = Fd = 24 \times 4[/tex].

Notice that in part (b), unlike part (a), we did not have to multiply by [tex]g[/tex] because we were given the weight (which is a force) and not the mass of the object.

Answer :

Final answer:

We calculate the work done when lifting an object by using the formula Work = Force x Distance. For example, when lifting a 1.2-kg book onto a 0.5 m high desk, the work done is 5.88 J. Similarly, when lifting a 24-lb weight 4 ft, the work done is 130.1206 J once the units are converted to SI.

Explanation:

The subject of this question is work and energy in physics, particularly how it is calculated when lifting objects. By considering force due to gravity (weight) and the height an object is lifted, we can calculate the work done.



Work Due To Gravity

To calculate the work done against gravity when lifting an object, we use the formula Work = Force x Distance. Here, Force = mass of the object x acceleration due to gravity (g) and Distance = height it is lifted.



Solving the Problems

  1. Work done lifting a 1.2-kg book to a 0.5 m high desk: Here, Force = 1.2 kg (mass of book) x 9.8 m/s² (acceleration due to gravity) = 11.76 N (Newton, the unit of force). Given that distance lifted = 0.5 m, Work = Force x Distance = 11.76 N x 0.5 m = 5.88 J (Joule, the unit of work).
  2. Work done lifting a 24-lb weight 4 ft high: Firstly, we have to convert lbs (a measure of weight) and ft to their SI units (kg and m respectively) for simplicity. If 1 lbs = 0.4536 kg and 1 ft = 0.3048 m, then 24 lbs = 10.886 kg and 4 ft = 1.2192 m. Now, applying the same steps as previous: Force = 10.886 kg x 9.8 m/s² = 106.6828 N. Subsequently, Work = Force x Distance = 106.6828 N x 1.2192 m = 130.1206 J.



The work you do lifting an object is equal to the object's gain in gravitational potential energy. This means that the work done against gravity, lifting an object up, is 'given back' when the object comes back down. This shows the efficiency and conservation involved in these physics concepts.

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Final answer:

To calculate the work done in lifting the book, multiply the force exerted (weight of the book) by the distance. The force exerted is equal to the mass of the book multiplied by the gravitational acceleration.

Explanation:

In order to calculate the work done in lifting the 1.2-kg book, we can use the formula:

Work = Force x Distance

The force exerted is equal to the weight of the book, which is given by the formula:

Force = mass x acceleration due to gravity

Substituting the values into the formulas, we have:

Force = 1.2 kg x 9.8 m/s^2

Distance = 0.5 m

Work = (1.2 kg x 9.8 m/s^2) x 0.5 m

Calculating this expression gives us the work done in lifting the book.

For the second part of the question, the force is given in pounds (lb). The formula remains the same, however, we don't need to multiply by the acceleration due to gravity. We can directly use the force and distance given to calculate the work.

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