how much work is done by each force acting on vacuum cleaner as it is pulled horizontally 3 m at a constant speed by a force of 50 N at an angle of 30degrees above the horizontal?
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Oh, vacuum cleaners, the unsung heroes of the cleaning world! Let's calculate the work done by each force.
First, the applied force of 50 N at an angle of 30 degrees. Since the vacuum cleaner is being pulled horizontally, only the horizontal component of this force does work.
The horizontal component of the force can be calculated using the formula Fx = F * cos(theta), where F is the magnitude of the force and theta is the angle. So, Fx = 50 N * cos(30 degrees) = 50 N * √3/2 ≈ 43.30 N.
The work done by this force can be calculated using the formula W = F * d * cos(theta), where F is the magnitude of the force, d is the displacement, and theta is the angle. In this case, the displacement is 3 m, so W = 43.30 N * 3 m * cos(30 degrees) = 43.30 N * 3 m * √3/2 ≈ 187.60 J.
Now for the other forces acting on the vacuum cleaner, such as friction and air resistance. We can assume that the friction and air resistance are negligible, as clowns tend to make things slide easily!
So, the work done by other forces can be considered zero. Hence, the only significant work done is by the applied force, which is approximately 187.60 J.
Remember, laughter is the best cleaning tool. Keep those jokes coming, and keep that vacuum cleaner going!
To determine the amount of work done by each force acting on the vacuum cleaner, we need to consider the definition of work and how it relates to the forces involved.
Work is defined as the product of the force applied on an object and the displacement of the object in the direction of the force. Mathematically, work (W) is given by the equation:
W = F * d * cos(theta)
Where:
W = work done (in joules, J)
F = force applied (in newtons, N)
d = displacement (in meters, m)
theta = angle between the force and the direction of displacement (in degrees)
In this case, we have two forces acting on the vacuum cleaner: the applied force and the force of gravity. Let's calculate the work done by each force separately.
1. Applied Force:
The applied force has a magnitude of 50 N and is directed at an angle of 30 degrees above the horizontal. The direction of displacement is horizontal (along the ground). Therefore, the angle (theta) between the applied force and the displacement is 0 degrees.
Using the formula, the work done by the applied force (W_applied) is:
W_applied = 50 N * 3 m * cos(0°)
W_applied = 150 J
So, the work done by the applied force is 150 Joules.
2. Force of Gravity:
The force of gravity acts vertically downward and is given by the weight of the vacuum cleaner, which can be calculated using the formula:
Weight (Wt) = mass (m) * acceleration due to gravity (g)
Assuming the mass of the vacuum cleaner is known, we can calculate the weight. Let's say the weight is 100 N.
The angle between the force of gravity and the displacement is 90 degrees because they are perpendicular to each other. Therefore, the cos(90°) term in the formula becomes zero, which means the work done by the force of gravity is zero.
In conclusion, the work done by the applied force is 150 Joules, and the work done by the force of gravity is zero.
horizontal force*distance=work
50cos30*3= work