Question

Jennifer lifts a 2.5 -kg carton of cat litter from the floor to a height of \(0.75 \mathrm{m} .\) (a) How much total work is done on the carton during this operation? Jennifer then pours \(1.2 \mathrm{kg}\) of the litter into the cat's litter box on the floor. (b) How much work is done by gravity on the $1.2 \mathrm{kg}$ of litter as it falls into the litter box?

Short answer

Question: Calculate the work done by Jennifer on lifting the carton and the work done by gravity on the litter falling into the box. Answer: (a) Work done on the carton by Jennifer: (2.5 kg x 9.81 m/s^2) x 0.75 m, (b) Work done by gravity on the litter falling into the litter box: (1.2 kg x 9.81 m/s^2) x 0.75 m.

Step-by-step solution

(a) Work done on the carton by Jennifer

To find the work done on the carton by Jennifer while lifting it to a height of 0.75 m, we first need to calculate the force exerted by her during the process, and for that, we will use the gravitational force formula. Force = mass x acceleration due to gravity Force = 2.5 kg x 9.81 m/s^2 Now we have the force exerted. The work done is given by the formula: Work done = force x displacement x cos(theta) Since Jennifer is lifting the carton vertically, the angle (theta) between the force and displacement is 0 degrees. So, cos(theta) = cos(0) = 1. Work done = Force x Displacement x 1 (since cos(0) = 1) Work done = (2.5 kg x 9.81 m/s^2) x 0.75 m

(b) Work done by gravity on the litter falling into the litter box

As the litter falls, we need to find the work done by gravity on the 1.2 kg of litter. Since the falling motion is vertical as well, the angle (theta) between the force and displacement is 0 degrees (cos(theta) = 1). We need to find the force exerted by gravity on the 1.2 kg of litter: Force = mass x acceleration due to gravity Force = 1.2 kg x 9.81 m/s^2 For the work done, we need to find the displacement as well. As the litter falls from the 0.75 m height, this is the displacement over which gravity acts: Displacement = 0.75 m Now, we can calculate the work done by gravity: Work done = force x displacement x cos(theta) Work done = (1.2 kg x 9.81 m/s^2) x 0.75 m x 1 (since cos(0) = 1)