A patialy moves along half the circumference of a circle of 1 meter radius. Calculate
the work done if the force at any point inclined at 60o to the tangent at that point has
5 New tones magnitude
You must mean 5 Newtons, not 5 New tones.
Force is not measured in tones.
What is a patialy?
If the problem that you meant to ask is:
<<A particle moves along half the circumference of a circle of 1 meter radius. Calculate the work done if the force at any point is inclined at 60 degrees to the tangent at that point, and has 5 Newtons magnitude.>>
If that is the question, then the answer is the product of the distance that the particle travels (pi meters) and the component of the force along the direction of motion (which is the tangent to the circle)
Work = pi * 5.0 N * cos60
= 2.5 pi joules
= 7.854 J
To calculate the work done, we need to use the formula:
Work = Force x Displacement x cos(theta)
Where:
- Force is the magnitude of the force acting on the object (5 N in this case)
- Displacement is the distance covered by the object (half the circumference of the circle, which is pi * radius)
- theta is the angle between the force vector and the displacement vector (60 degrees in this case)
First, let's calculate the displacement:
The circumference of a circle is given by the formula: Circumference = 2 * pi * radius
So, the displacement will be: Displacement = 0.5 * (2 * pi * radius) = pi * radius
Next, let's calculate the work done using the formula:
Work = Force x Displacement x cos(theta)
Now we have all the values we need to calculate the work done:
Force = 5 N
Displacement = pi * radius
theta = 60 degrees
Substituting the values:
Work = 5 N * (pi * radius) * cos(60 degrees)
To compute the final value, we need to convert the angle from degrees to radians because the cosine function in most programming or mathematical languages uses radians. We can convert degrees to radians using the formula: radians = (degrees * pi) / 180.
So, in this case:
theta = (60 degrees * pi) / 180 = pi/3 radians
Substituting the value of theta back into the formula:
Work = 5 N * (pi * radius) * cos(pi/3)
Now, we can calculate the work done by multiplying all the values:
Work = 5 N * (pi * 1 meter) * cos(pi/3)
Finally, we can simplify and calculate the work done:
Work = 5 N * pi * cos(pi/3)
Thus, the work done will be the product of these values: 5 N * pi * cos(pi/3).