The initial velocity of a 4.0-kg box is 11 m/s, due west. After the box slides 4.0 m horizontally, its speed is 1.5 m/s. Determine the magnitude and the direction of the non-conservative force acting on the box as it slides
Work done against friction (F * X) equals loss of kinetic energy.
Solve for F
V = 4.0 meters
To determine the magnitude and direction of the non-conservative force acting on the box, we need to apply the work-energy principle.
The work-energy principle states that the work done on an object is equal to its change in kinetic energy. Mathematically, it is expressed as:
Work = Change in Kinetic Energy
In this case, the non-conservative force causes a change in the kinetic energy of the box. We can calculate the work done using the following formula:
Work = Force * Distance * cos(theta)
where Force is the applied force, Distance is the displacement of the box, and theta is the angle between the force and the displacement vectors.
Since the force acts horizontally, the angle (theta) between the force and displacement vectors is 0 degrees, and cos(0°) = 1.
Therefore, the formula for work simplifies to:
Work = Force * Distance
The work done is also equal to the change in kinetic energy:
Work = Change in Kinetic Energy
Since the problem provides the initial velocity, final velocity, and distance traveled, we can calculate the change in kinetic energy:
Change in Kinetic Energy = (1/2) * Mass * (Final Velocity^2 - Initial Velocity^2)
Plugging in the given values:
Mass = 4.0 kg
Initial Velocity = 11 m/s
Final Velocity = 1.5 m/s
Change in Kinetic Energy = (1/2) * 4.0 kg * (1.5 m/s^2 - 11 m/s^2)
Calculating the change in kinetic energy:
Change in Kinetic Energy = (1/2) * 4.0 kg * (-9.5 m/s^2) = -19 J (Joules)
Since the work done (force * distance) is equal to the change in kinetic energy, we can rearrange the equation to solve for the force:
Force = Change in Kinetic Energy / Distance
Force = -19 J / 4.0 m = -4.75 N (Newton)
The magnitude of the non-conservative force acting on the box is 4.75 N.
Since the question asks for the direction of the force, we can determine it based on the given information that the initial velocity is due west and the final velocity is in the opposite direction (since the box is slowing down). Therefore, the force is acting in the direction of the initial velocity, which is due west.
Hence, the direction of the non-conservative force acting on the box is west.