You are in the supermarket, pushing a cart with a force of 79 Newtons in the horizontal direction. There is a constant force of kinetic friction operating on the cart of 14.2 Newtons.
Calculate the net work done on the cart, if the cart is displaced 1.2 metres in a straight line.
work done on cart=79*1.2m-14.2*1.2
To calculate the net work done on the cart, we need to use the work-energy principle, which states that the net work done on an object is equal to the change in its kinetic energy.
The net work done on the cart can be calculated using the formula:
Net work = Force applied x Distance moved x cos(theta)
In this case, the applied force is the force with which you push the cart, which is 79 Newtons, and the distance moved is 1.2 meters. The angle theta between the applied force and the direction of motion is 0 degrees since the cart is being displaced in a straight line horizontally.
Therefore, the formula simplifies to:
Net work = Force applied x Distance moved x cos(0)
Net work = 79 N x 1.2 m x cos(0)
Next, we need to consider the force of kinetic friction operating on the cart, which is 14.2 Newtons. Since this force is acting opposite to the direction of motion, it will do negative work.
Negative work done by the force of friction = Force of friction x Distance moved x cos(180)
Negative work done by the force of friction = 14.2 N x 1.2 m x cos(180)
Finally, we can calculate the net work done on the cart by subtracting the negative work done by the force of friction from the positive work done by the applied force:
Net work = (79 N x 1.2 m x cos(0)) - (14.2 N x 1.2 m x cos(180))
Net work = 94.8 Joules - (-17.04 Joules)
Net work = 94.8 Joules + 17.04 Joules
Net work = 111.84 Joules
Therefore, the net work done on the cart is 111.84 Joules.