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Lesson Worksheet: The Work–Energy Principle Mathematics
In this worksheet, we will practice using the work–energy principle to solve problems of motion of a particle.
A tram of mass 2 metric tons was being towed by a rope inclined at an angle of to the track against a resistance of 20 kg-wt. Given that the tension in the rope was 121 kg-wt, use the work–energy principle to find the kinetic energy of the tram and its speed after moving a distance of 16 m. Take the acceleration due to gravity to be .
Two bullets of equal mass were fired toward a target at the same speed but in opposite directions. The target was formed of two different pieces of metal stuck together. The first was 9 cm thick, and the second was 12 cm thick. When the bullets hit the target, the first one passed through the first layer and embedded 4 cm into the second before it stopped, whereas the other bullet passed through the second layer and embedded 5 cm into the first layer before it stopped. Using the work–energy principle, calculate the ratio of the resistance of the first metallic layer to that of the second.