 Mathematical and Physical Journal
for High Schools
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# Exercises and problems in PhysicsNovember 2002 ## Experimental problem

M. 237. Make a 1.5 m-long line pendulum using a table-tennis ball as the weight. How does the work done by the aerodynamic drag (the energy lost) depend on the starting height h? What is the average power of the aerodynamic force during a half swing? (6 points) ## Theoretical problems

It is allowed to send solutions for any number of problems, but final scores of students of grades 9-12 are computed from the 5 best score in each month. Final scores of students of grades 1-8 are computed from the 3 best scores in each month.

P. 3561. According to a car safety advertisement a 50 km/h collision into a wall has the same result as falling off the top of a four-storey building. What storey height did they think of? (3 points)

P. 3562. In a fruit farm the crates are conveyed on steel plates dragged by tractors. The mass of a steel plate is 20 kg and 400 kg of fruit is piled on it. The friction coefficient between the plate and the soil is 0.6. To what extent does the steel plate heat up on a 100 meter road if the internal energy of the steel plate is increased by 40% of the work done by the friction? (3 points)

P. 3563. There are two cars following each other on a narrow straight road. Their speed is 72 km/h each. The leading one begins to brake and stops with constant deceleration while his velocity decreases 5 m/s a second. The response time of the other driver is 1 second, and he can decrease his velocity by 4 m/s a second. a) What distance should there be at least between the two cars to avoid a collision? b) If they keep the minimally safe distance, how long will it take them to be at a 22 m distance of each other after the fist one begins to brake? (4 points)

P. 3564. How many balloons of a 25 cm diameter can be inflated from a 0.1 m3 volume gas cylinder filled with helium at a pressure of 1.5x107 Pa? The gas pressure in a balloon rises to 1.02x105 Pa when the temperature of the gas reaches the temperature of the environment. The gas cylinder has been in the place where the balloons are filled for days. (4 points)

P. 3565. We want to cool down 15 l of 80 oC water to 25 oC by putting 0 oC ice into it. What minimum volume should the vessel have to prevent the water from overflowing at the rim? (3 points)

P. 3566. We want to throw a weight of 5 kg over a 1.5 m high wall, starting from ground level at a 2 m distance from the wall. a) what should the direction of the 8 m/s initial velocity be to throw the weight the furthest beyond the wall? What is this distance? b) What is the lowest energy to use for throwing the weight over the wall? What is the direction of the initial velocity in this case? (5 points)

P. 3567. Determine the size of the two hatched areas in the figure without using the integral calculus, by some simple physical reasoning. (5 points) P. 3568. We fix a line pendulum with a pointlike weight of mass m to a horizontal metal ceiling. The period of the pendulum for small amplitudes is T1. Then we put some electric charge on the weight and make it swing with a small amplitude again. The period now is T2. What is the charge put on the weight? (The data: m= 5 g, T1=2.02 s, T2=2.03 s, g=9.81 m/s2.) (5 points)

P. 3569. There is a 1.12 A electric current going through a working discharge tube filled with hydrogen gas. How many electrons pass the cross-section of the tube in one second if the number of electrons leaving the cathode is 3x1018 a second? (4 points)

P. 3570. We connect an R resistance, an L inductor device and a C capacitor after a sinusoidal generator of voltage U in a serial arrangement. The inductivity is adjustable. When it is increased, the current first increases then it begins to decrease. The highest current reached is I0, and then the voltage of the coil is U0. Increasing the inductivity further, the voltage of the coil reaches a maximum of Umax , and then begins to decrease. Determine the Umax /U0 ratio and calculate its value when $\displaystyle R=2\sqrt{2}X_C$. (5 points)