Math Problem Statement
An object of mass 10 kg is being dragged at an angle of 60° with the ground. This causes the object to move with a constant velocity of 4m. Determine the work done by it. [frictional co efficient ug=0.2]
Solution
To find the work done on the object being dragged at a constant velocity, we need to consider the forces acting on it.
-
Weight of the object (W):
-
Normal force (N):
The vertical component of the pulling force affects the normal force. The normal force is given by:
where is the pulling force, and is the angle. -
Frictional force (F_f):
where . -
Force required to overcome friction:
Since the object moves at constant velocity, the horizontal pulling force equals the frictional force:
.
Using these relations, you can calculate the work done by the pulling force, considering the distance moved (4 m).
Let's break it down:
- Calculate the normal force and frictional force.
- The work done (W) by the pulling force can be calculated as:
,
since the angle of displacement and force direction is the same.
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Math Problem Analysis
Mathematical Concepts
Physics
Dynamics
Work-Energy Principle
Formulas
W = F · d · cos(θ)
F_f = μ · N
N = W - (F · sin(θ))
Theorems
Work-Energy Theorem
Suitable Grade Level
Grades 10-12
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