A record company executive is on his way to a TV interview and is carrying a promotional CD in his briefcase. The mass of the briefcase and its contents is 4.00 kg. The executive realizes that he is going to be late. Starting from rest, he starts to run, reaching a speed of 2.50 m/s. What is the work done by the executive on the briefcase during this time? Neglect air resistance.
W=(1/2)mv²
To find the work done by the executive on the briefcase, we need to use the formula for work:
Work = force × displacement × cos(θ)
In this case, the force is the force exerted by the executive while running, the displacement is the distance traveled, and θ is the angle between the force and the direction of displacement. Since the executive is running in a straight line, the angle θ is 0, and cos(θ) becomes 1.
First, we need to find the force exerted by the executive. We can do this using Newton's second law:
Force = mass × acceleration
The mass of the briefcase and its contents is given as 4.00 kg. Since the executive is carrying the briefcase and running, we need to consider the total mass that includes the executive and the briefcase. Let's assume a hypothetical mass for the executive, say 70 kg.
Now, we can find the acceleration using the speed and the initial velocity (0 m/s):
Acceleration = (final velocity - initial velocity) / time = (2.50 m/s - 0 m/s) / t = 2.50 m/s / t
Next, let's rewrite Newton's second law to solve for force:
Force = mass × acceleration = (4.00 kg + 70 kg) × (2.50 m/s / t)
Finally, we can substitute the force into the work formula:
Work = force × displacement × cos(θ) = (74.00 kg) × (2.50 m/s / t) × displacement × cos(0)
Since we don't have the exact distance traveled, we cannot calculate the work done by the executive on the briefcase without that information.