In physics, work is defined as a force acting upon an object to cause a displacement. There are three key words in this definition - force, displacement, and cause. In order for a force to qualify as having donework on an object, there must be a displacement and the force must cause the displacement. There are several good examples of work which can be observed in everyday life

a) a horse pulling a plow through the fields

b) a father pushing a grocery cart down the aisle of a grocery store

c) a freshman lifting a backpack full of books upon her shoulder

d) a weightlifter lifting a barbell above her head, a shot-put launching the shot, etc.

Q1. In each case described above there is a force exerted upon an object to cause that object to be displaced. Explain what the force is and the direction of the displacement.

Q2. Read the following five statements and determine whether or not they represent examples of work. For each example explain your reason.

a) A teacher applies a force to a wall and becomes exhausted.

b) A book falls off a table and free falls to the ground.

c) A waiter carries a tray full of meals above his head by one arm across the room.

d) A rocket accelerates through space.

 

Here F = force, d = displacement, and the angle (theta) is defined as the angle between the force and the displacement vector. The angle is not just any old angle, but rather a very specific angle. The angle measure is defined as the angle between the force and the displacement.

Q3. Using your calculator find the cos of the following angles:

cos 45˚, cos 80˚, cos 90˚, cos 0˚, cos 75˚

Examples to show three different angles:

Ex. 1 A force acts rightward upon an object as it is displaced rightward. In such an instance, the force the displacement are in the same direction.
Q4. The angle between F and d is 0 degrees. What is the formula for work when the angle is 0˚?

Ex. 2 A force acts leftward upon an object which is displaced rightward. In such an instance, the force vector and the displacement vector are in the opposite direction. Thus, the angle between F and d is 180 degrees.
Q5. What is the formula for work when the angle is 180˚?

Ex. 3 A force acts upward upon an object as it is displaced rightward. In such an instance, the force vector and the displacement vector are at right angles to each other. Thus, the angle between F and d is 90 degrees.
Q6. What is the formula for work when the angle is 90˚?

Example 3 above involves a situation similar to the waiter who carried a tray full of meals above his head by one arm across the room. It was mentioned earlier that the waiter does not do work upon the tray as he carries it across the room. The force supplied by the waiter on the tray is an upward force and the displacement of the tray is a horizontal displacement. As such, the angle between the force and the displacement is 90 degrees. If the work done by the waiter on the tray were to be calculated, then the results would be 0. Regardless of the magnitude of the force and displacement, F*d*cosine 90 degrees is 0 (since the cosine of 90 degrees is 0). A vertical force can never cause a horizontal displacement; thus, a vertical force does not do work on a horizontally displaced object!!

Suppose that a car traveled up three different roadways (each with varying incline angle or slope) from the base of a mountain to the summit of the mountain.

Q7. Which path would require the most gasoline (or energy)? Would the steepest path (path AD) require the most gasoline or would the least steep path (path BD) require the most gasoline? Or would each path require the same amount of gasoline?

This situation can be simulated by use of a simple physics lab in which a force is applied to raise a cart up an incline at constant speed to the top of a seat. Three different incline angles could be used to represent the three different paths up the mountain. The seat top represents the summit of the mountain. And the amount of gasoline (or energy) required to ascend from the base of the mountain to the summit of the mountain would be represented by the amount of work done on the cart to raise it from the floor to the seat top. The amount of work done to raise the cart from the floor to the seat top is dependent upon the force applied to the cart and the displacement caused by this force. Typical results of such a physics lab are depicted in the animation below.

Q8. Explain the results of the above animation.

Q9. Apply the work equation to determine the amount of work done by the applied force in each of the three situations described below. Show the work for each question!

Q11. Ben Travlun carries a 200-N suitcase up three flights of stairs (a height of 10.0 m) and then pushes it with a horizontal force of 50.0 N at a constant speed for a horizontal distance of 35.0 meters. How much work does Ben do on his suitcase during this entire motion?

Q13. How much work is done by an applied force to lift a 15-Newton block 3.0 meters vertically at a constant speed?

Q14. A student with a mass of 80.0 kg runs up three flights of stairs. The student has gone a vertical distance of 8.0 m. Determine the amount of work done by the student to elevate his body to this height.

Q15. A tired squirrel (mass of 1 kg) does push-ups by applying a force to elevate its center-of-mass by 0.05 m. Determine the number of push-ups which a tired squirrel must do in order to do a mere 5.0 Joules of work.