A block of mass 10 kg, moving in x direction with a constant speed of 10 ms-1, is subjected to a retarding force F = 0.1 x J/m during its travel from x = 20 m to 30 m. Its final KE will be:

  • Option 1)

    275 J

  • Option 2)

    250 J

  • Option 3)

    475 J

  • Option 4)

    450 J

 

Answers (2)

As we discussed in

Net work done by all the forces give the change in kinetic energy -

W=frac{1}{2}mv^{2}-frac{1}{2}mv{_{0}}^{2}

W= k_{f}-k_{i}

- wherein

m=mass : of: the: body

v_{0}= initial: velocity

v= final: velocity

 

 

 

Definition of work done by variable force -

W=int vec{F}cdot vec{ds}

- wherein

vec{F} is variable force and vec{ds} is small displacement

 

 k_{i}=\frac{1}{2}m{v_{i}}^{2}=\frac{1}{2}\times 10\times \left ( 10 \right )^{2}=500J

w= \int_{x_{1}}^{x_{2}}f_{r}.dx=\int_{20}^{30}-0.1x dx= -0.1\left [ \frac{x^{2}}{2} \right ]^{30}_{20}= -0.1\left [ \frac{900-400}{2} \right ]= -25J

w= k_{f}-k_{i}=k_{f}=w+k_{i}

-25 J+500 J = 475 J


Option 1)

275 J

Incorrect Option

Option 2)

250 J

Incorrect Option

Option 3)

475 J

Correct Option

Option 4)

450 J

Incorrect Option

475J

 

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