calculate the work done if a force of 10N applied at an angle of 30 0degree to the horizontal moves the body through a distance of 0.05m?
effective force in direction of motion: 10 cos30°
and, as always,
work = force * distance
Well, to calculate the work done, we need to use the formula:
Work = Force × Distance × cos(θ)
Where:
- Force is the applied force (10N)
- Distance is the displacement of the body (0.05m)
- θ is the angle between the force and the direction of displacement (30 degrees)
So, plugging in the values:
Work = 10N × 0.05m × cos(30 degrees)
Now, let's see if we can bring some humor into the equation. Hmm...
Why did the force go to therapy?
Because it had trouble finding its direction!
But let's continue with the calculation:
Work = 10N × 0.05m × 0.866
Work ≈ 0.0433 Joules
So, the work done by the force is approximately 0.0433 Joules. I hope that brings a little humor to your work!
To calculate the work done, you can use the formula:
Work (W) = Force (F) x Distance (d) x cos(theta)
where
- W is the work done,
- F is the force applied,
- d is the distance moved, and
- theta is the angle between the force and the horizontal direction.
Given:
- Force (F) = 10 N
- Distance (d) = 0.05 m
- Angle (theta) = 30 degrees
First, we need to convert the angle from degrees to radians:
theta_radians = theta * (pi / 180)
theta_radians = 30 * (pi / 180)
theta_radians = 0.5236 radians (rounded to four decimal places)
Now, we can calculate the work done:
W = F * d * cos(theta_radians)
W = 10 N * 0.05 m * cos(0.5236 radians)
W = 10 N * 0.05 m * 0.8660 (rounded to four decimal places, where cos(0.5236 radians) is approximately 0.8660)
W = 0.0433 Joules (rounded to four decimal places)
Therefore, the work done by the force of 10 N, applied at an angle of 30 degrees to the horizontal, moving the body through a distance of 0.05 m, is approximately 0.0433 Joules.
To calculate the work done, we will use the formula:
Work = Force * Distance * cos(theta)
Where:
- Work is the amount of energy transferred when a force moves an object.
- Force is the applied force (10N in this case).
- Distance is the distance over which the force is applied (0.05m in this case).
- theta is the angle between the applied force and the direction of motion (30 degrees in this case).
First, we need to convert the angle from degrees to radians since cosine function takes input in radians. We can use the formula:
radian = degree * (π / 180)
So, the angle in radians will be:
theta = 30 * (π / 180) = 0.5236 radians
Next, we can substitute the values into the formula:
Work = 10N * 0.05m * cos(0.5236 radians)
Use a calculator to find the value of cos(0.5236 radians). Round the result to an appropriate number of significant figures, let's say 2 decimal places.
Finally, perform the calculation:
Work ≈ 10N * 0.05m * cos(0.5236 radians) ≈ [calculate the result]
Therefore, the work done by the force of 10N, applied at an angle of 30 degrees to the horizontal, moving the body through a distance of 0.05m is approximately [calculated result] Joules.