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.

  1. Weight of the object (W):
    W=mg=10kg9.81m/s2=98.1NW = m \cdot g = 10 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 = 98.1 \, \text{N}

  2. Normal force (N):
    The vertical component of the pulling force affects the normal force. The normal force is given by:
    N=WFy=W(Fsinθ)N = W - F_{y} = W - (F \cdot \sin \theta)
    where FF is the pulling force, and θ\theta is the angle.

  3. Frictional force (F_f):
    Ff=μNF_f = \mu \cdot N
    where μ=0.2\mu = 0.2.

  4. Force required to overcome friction:
    Since the object moves at constant velocity, the horizontal pulling force equals the frictional force:
    Fcosθ=FfF \cdot \cos \theta = F_f.

Using these relations, you can calculate the work done by the pulling force, considering the distance moved (4 m).

Let's break it down:

  1. Calculate the normal force and frictional force.
  2. The work done (W) by the pulling force can be calculated as:
    W=Fdcos(0)=FdW = F \cdot d \cdot \cos(0) = F \cdot d,
    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