Mass of the body, m = 2 kg
Applied force, F = 7 N
Coefficient of kinetic friction, \(\mu\) = 0.1
Initial velocity, u = 0
Time, t = 10 s
The acceleration produced in the body by the applied force is given by Newton’s second law of motion as:
a' =\(\frac{F}{m}\) = \(\frac{7}{2}\) = 3.5 \(m/s^2\)
Frictional force is given as:
f = \(\mu\)mg = 0.1 × 2 × 9.8 = – 1.96 N
The acceleration produced by the frictional force:
a'' = \(-\frac{1.96}{2}\)= -0.98 \(m/s^2\)
Total acceleration of the body:
a = a' + a'' = 3.5 + (- 0.98) = 2.52 \(m/s^2\)
The distance travelled by the body is given by the equation of motion:
s = ut + \(\frac{1}{2}\) at2
= \(0\) + \(\frac{1}{2}\) × \(2.52\) × \((10)^2\) = \(126\) m
Work done by the applied force, \(W_a\) = \(F\times s\)= 7 × 126 = 882 J
Work done by the frictional force, \(W_f\) = \(F\times s\) = - 1.96 × 126 = - 247 J
Net force = 7 + (–1.96) = 5.04 N
Work done by the net force,\(W_{net}\) = 5.04 × 126 = 635 J
From the first equation of motion, final velocity can be calculated as :
v = u + at = 0 + 2.52 × 10 = 25.2 \(m/s\)
Change in kinetic energy = \(\frac{1}{2}mv^2-\frac{1}{2}mu^2\) = \(\frac{1}{2}\times (v^2-u^2)\)
= \((25.2)^2-0^2\)= 635 J
A thermodynamic system is taken through a cyclic process as shown in the PV diagram. The total work done in the process is:
Find the mean and variance for the following frequency distribution.
Classes | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
Frequencies | 5 | 8 | 15 | 16 | 6 |
Work is the product of the component of the force in the direction of the displacement and the magnitude of this displacement.
W = Force × Distance
Where,
Work (W) is equal to the force (f) time the distance.
W = F d Cos θ
Where,
W = Amount of work, F = Vector of force, D = Magnitude of displacement, and θ = Angle between the vector of force and vector of displacement.
The SI unit for the work is the joule (J), and it is defined as the work done by a force of 1 Newton in moving an object for a distance of one unit meter in the direction of the force.
Work formula is used to measure the amount of work done, force, or displacement in any maths or real-life problem. It is written as in Newton meter or Nm.