A 7453 N piano is to be pushed up a(n) 4.04 m frictionless plank that makes an angle of 25.9� with the horizontal.
Calculate the work done in sliding the piano up the plank at a slow constant rate.
Answer in units of J
Well, pushing a piano up a hill certainly sounds like a workout! Let's calculate the work done.
First, we need to find the component of the piano's weight that acts in the direction of the plank. This can be calculated using the equation:
Force parallel = Force gravity * sin(angle)
Force gravity = 7453 N (given)
Angle = 25.9 degrees (given)
Force parallel = 7453 N * sin(25.9)
Now, let's calculate the work done by multiplying the force parallel by the displacement:
Work done = Force parallel * displacement
Displacement = 4.04 m (given)
Work done = (7453 N * sin(25.9)) * 4.04
Now, I'm not a calculator, but you can go ahead and do the math to find the answer in units of joules (J).
To calculate the work done in sliding the piano up the plank, we can use the formula:
Work = force × displacement × cos(θ)
Where:
- Work is the work done in Joules (J).
- force is the force applied to the piano, which is the weight of the piano in this case. It is given as 7453 N.
- displacement is the distance over which the force is applied, which is the length of the plank in this case. It is given as 4.04 m.
- θ is the angle between the force and the displacement, which is the angle of the plank with the horizontal. It is given as 25.9 degrees.
Plugging in the values:
Work = 7453 N × 4.04 m × cos(25.9°)
Using a calculator, we can evaluate the cosine function and calculate the work:
Work = 7453 N × 4.04 m × 0.901
Work ≈ 27044.9 J
Therefore, the work done in sliding the piano up the plank at a slow constant rate is approximately 27044.9 Joules.
To calculate the work done in sliding the piano up the plank, we need to use the formula for work:
Work = Force × Distance × cos(θ)
Where:
- Force is the component of the force acting along the direction of displacement,
- Distance is the displacement or distance covered in the direction of the force,
- θ is the angle between the force and the direction of displacement.
In this case, the force acting along the direction of displacement is the weight of the piano, which is given as 7453 N. The distance covered in the direction of the force is the displacement of the piano up the plank, which is given as 4.04 m. The angle between the force and the direction of displacement is 25.9 degrees.
First, we need to find the component of the weight of the piano along the direction of displacement. We can do this by multiplying the weight by the cosine of the angle:
Component of force = Force × cos(θ)
Component of force = 7453 N × cos(25.9 degrees)
Next, we can substitute the values into the work formula to calculate the work done:
Work = Component of force × Distance × cos(θ)
Work = (7453 N × cos(25.9 degrees)) × 4.04 m × cos(25.9 degrees)
Finally, we can simplify and calculate the numerical value using a calculator:
Work ≈ (7453 N × 0.8926) × 4.04 m × 0.8926
Work ≈ 23924.8408 N·m
Since the unit of work is measured in joules (J), we need to convert N·m to J. Since 1 joule equals 1 N·m, the work done is approximately 23924.8408 J.
Therefore, the work done in sliding the piano up the plank at a slow constant rate is approximately 23924.8408 J.
m*g = 7453 N.
m*g = 7453 N.
Fp = 7453*sin25.9 = 3256 N. = Force
parallel to incline.
Fap = Fp = 3256 N. = Force applied.
Work = F * d = 3256 * 4.04 = 13,152 J.
fp =