A crate of mass 20kg was moved up a rough plane inclined at 60° to the ground. If the crate was moved up a distance of 5m after 10secs, determine the total work done?
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To determine the total work done, we need to calculate the work done against gravity (the weight of the crate) and the work done against friction (due to the rough surface of the inclined plane).
1. First, let's calculate the work done against gravity (Wg). The formula for work done against gravity is Wg = m * g * h, where m is the mass of the crate, g is the acceleration due to gravity (9.8 m/s^2), and h is the vertical height the crate is moved.
Given:
- Mass of the crate (m) = 20 kg
- Angle of inclined plane (θ) = 60°
- Distance moved along the inclined plane (s) = 5 m
To find the vertical height (h) moved, we can use the formula h = s * sin(θ). Substituting the given values, we get h = 5 m * sin(60°) = 5 m * √3/2 = (5√3)/2 m.
Now, we can calculate the work done against gravity:
Wg = m * g * h = 20 kg * 9.8 m/s^2 * (5√3)/2 m.
2. Next, let's calculate the work done against friction (Wf). The formula for work done against friction is Wf = μ * m * g * d, where μ is the coefficient of friction between the crate and the rough inclined plane, and d is the distance moved horizontally.
Since the crate is moved up a rough plane, there will be friction acting against the motion. However, we cannot determine the coefficient of friction (μ) from the given information, and it is assumed to be unknown.
Therefore, without the value of μ, we are unable to calculate the work done against friction (Wf) accurately.
3. Finally, determine the total work done (W).
The total work done (W) is the sum of the work done against gravity (Wg) and the work done against friction (Wf), assuming no other external forces are involved.
W = Wg + Wf.
However, since we do not have the value of the coefficient of friction (μ), we can only calculate the work done against gravity (Wg).
Therefore, the total work done cannot be determined accurately without knowing the coefficient of friction (μ) between the crate and the rough inclined plane.