the initial velocity of a 4 kg box is 11 m/s, due west. after the box slides 4 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.
59 due east
KE2-KE1=W(fr) =F•s
mv₂²/2 - mv₁²/2 = F•s
Solve for F
To determine the magnitude and direction of the non-conservative force acting on the box as it slides, we can use the work-energy principle. The work-energy principle states that the work done by non-conservative forces is equal to the change in kinetic energy.
1. First, let's calculate the initial kinetic energy (KEi) and final kinetic energy (KEf) of the box:
- Mass of the box (m) = 4 kg
- Initial velocity (vi) = 11 m/s
- Final velocity (vf) = 1.5 m/s
Using the formula for kinetic energy (KE = 0.5 * m * v^2), we have:
- KEi = 0.5 * 4 kg * (11 m/s)^2
- KEf = 0.5 * 4 kg * (1.5 m/s)^2
2. Next, let's calculate the work done by non-conservative forces, which is equal to the change in kinetic energy:
- Work (W) = KEf - KEi
3. Finally, to find the magnitude and direction of the non-conservative force, we need to know the displacement of the box and the angle between the force and the displacement vector. From the given information, we know that the box slides 4 m horizontally. If the force and displacement are in the same direction, the angle theta between them is 0 degrees.
- Displacement (d) = 4 m
- Angle (θ) = 0 degrees
The magnitude of the non-conservative force can be calculated using the formula:
- Magnitude of Force (F) = W / d
The direction of the non-conservative force is given by the angle theta:
- Direction of Force (θ) = 0 degrees (due west)
To sum up:
- Magnitude of the non-conservative force acting on the box as it slides is given by: F = (KEf - KEi) / d
- Direction of the non-conservative force acting on the box as it slides is due west.
To determine the magnitude and direction of the non-conservative force acting on the box as it slides, we need to use the work-energy principle.
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. Mathematically, it can be written as:
Work = Change in Kinetic Energy
The initial kinetic energy (KEi) of the box can be calculated using the equation:
KEi = (1/2) * mass * (initial velocity)^2
Substituting the given values:
KEi = (1/2) * 4 kg * (11 m/s)^2 = 242 Joules
Similarly, the final kinetic energy (KEf) can be calculated using the equation:
KEf = (1/2) * mass * (final velocity)^2
Substituting the given values:
KEf = (1/2) * 4 kg * (1.5 m/s)^2 = 4.5 Joules
The change in kinetic energy (ΔKE) can be calculated as:
ΔKE = KEf - KEi = 4.5 Joules - 242 Joules = -237.5 Joules
Since the change in kinetic energy is negative, it means that work has been done on the box by a non-conservative force.
Now, let's determine the magnitude and direction of the non-conservative force. We know that work is given by the equation:
Work = Force * displacement * cos(θ)
The non-conservative force is the force that is doing work on the box. Therefore, the work done by the non-conservative force can be calculated as:
Work = ΔKE = -237.5 Joules
The displacement (d) of the box is given as 4 m, and the angle (θ) between the force and displacement is 180 degrees (due west direction).
Substituting the values:
-237.5 Joules = Force * 4 m * cos(180°)
Cos(180°) = -1, so the equation becomes:
-237.5 Joules = Force * 4 m * (-1)
Simplifying the equation, we get:
Force = -237.5 Joules / (4 m * (-1)) = 59.375 N
Therefore, the magnitude of the non-conservative force acting on the box is 59.375 Newtons.
Since the angle is 180 degrees (due west), the direction of the non-conservative force is also west.