Kinetic and potential energy, work-energy theorem
- The kinetic energies of two similar cars A and B are 100 J and 225 J respectively. On applying breaks, car A stops after 1000 m and car B stops after 1500 m. If F_A and F_B are the forces applied by the breaks on cars A and B, respectively, then the… Answer: 2. 2/3 Key idea: by the work-energy theorem, the brake force does work equal to the kinetic energy lost: F d = K . F_A=100/1000=0.1\... 1
- A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field E. Due to the force q E, its velocity increases from 0 to 6 m/s in one second duration. At that instant the direction of the fiel… Answer: 3. 1 m/s, 3 m/s Phase 1 (0 to 1 s): a=6\ m/s² , displacement =1/2·6·1=3 m, ending at 6 m/s. Phase 2 (1 to 3 s): the acceleration rev... 1
- Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m/s. Take 'g' constant with a value 10 m/s^2. The work done by the (i) gravitational force and the (ii) resistive force of air is : Answer: 3. (i) 10 J (ii) - 8.75 J Key idea: use work-energy theorem: W_g+W_air=Δ KE . (i) W_g=mgh=0.001×10×1000=10 J. Δ KE=1/2(0.001)(50)²=1... 1
- A body of mass 1 kg begins to move under the action of a time dependent force F = (2t i + 3t^2 j) N, where i and j are unit vectors along x and y axis. What power will be developed by the force at the time t ? Answer: 4. (2t³ + 3t⁵) W Key idea: power P=vec F·vec v ; find vec v by integrating vec a=vec F/m . vec a=2that i+3t²hat j (m = 1 kg), so vec... 1