**G. 587.** For \(\displaystyle t\) seconds a force \(\displaystyle F\) is exerted on an easily moveable trolley of mass \(\displaystyle m\). The trolley was initially at rest, and after the force ceased the trolley moves freely along the horizontal path. What is the distance covered by the trolley during a time of \(\displaystyle 2t\), measured from the beginning of the motion?

*Data:* \(\displaystyle m=1.6\) kg, \(\displaystyle F=2\) N, \(\displaystyle t=0.5\) s.

(3 points)

This problem is for grade 1 - 9 students only.

**P. 4888.** The area of the plates of a parallel plate capacitor is 2 dm\(\displaystyle {}^2\), and their distance is 1 cm. The condenser is charged to a potential difference of 1000 V and then it is disconnected from the voltage source.

\(\displaystyle a)\) What is the surface density of the charge on the plates?

\(\displaystyle b)\) What is the magnitude of the force between the plates?

\(\displaystyle c)\) By what amount does the energy of the capacitor increase if the plates are displaced to a distance of 1.5 cm?

(4 points)

**P. 4890.** A point-like object of mass \(\displaystyle m=1\) g and of charge \(\displaystyle Q=2\cdot 10^{-7}\) C is in uniform vertically upward electric field of magnitude \(\displaystyle E=6\cdot 10^4\) V/m. The object is given an initial downward speed of \(\displaystyle v_0=2\) m/s at an angle of \(\displaystyle \varphi=30^\circ\) with respect to the vertical.

\(\displaystyle a)\) To what maximum depth measured from the level of projection does it go down?

\(\displaystyle b)\) How much time elapses until it reaches the lowest position?

\(\displaystyle c)\) What will its distance from its starting point be \(\displaystyle t=1.8\) s after it was started?

(5 points)

**P. 4893.** Bodies of different masses and different velocities are colliding with objects of mass \(\displaystyle M\), which are at rest. The collisions are head-on, totally elastic and the speed of each body is much less than the speed of light.

\(\displaystyle a)\) Determine the energy \(\displaystyle W\) given to the initially stationary object, in terms of the energy \(\displaystyle E\), and linear momentum \(\displaystyle I\) of the object which collides with it.

\(\displaystyle b)\) Sketch the graph of the function \(\displaystyle W(E,I)\) for fixed linear momentum \(\displaystyle I_0\), then for fixed energy \(\displaystyle E_0\).

\(\displaystyle c)\) Is it possible that an object having less energy gives more energy to the initially stationary body another one having more energy?

(6 points)