Worksheet: The Work–Energy Principle
In this worksheet, we will practice using the work–energy principle to solve problems of motion of a particle.
A body of mass 15 kg fell from a height of 15 m above the ground. Using the work-energy principle, find its kinetic energy just before it hit the ground. Consider the acceleration due to gravity to be 9.8 m/s2 .
Two bullets of equal mass were fired at the same speed into the opposite sides of a target. The target was formed of two different pieces of metal stuck together. The first was 10 cm thick, and the second was 14 cm thick. When the bullets hit the target, the first one passed through the first layer and embedded 8 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 , where is the resistance of the first metallic layer, and is that of the second.
The coordinates of the points and are and . A body of unit mass moved from to in the direction of under the action of the force , where force units. Given that the body started moving from rest, use the work-energy principle to find its kinetic energy at point .
A body of mass 4 kg is projected at 3.3 m/s up the line of greatest slope of a smooth inclined plane. Using the work-energy principle, find the work done by the body’s weight from the start of its motion until it came to a momentary rest.
A particle of mass 100 g was projected vertically upward at 20 m/s from a point on the ground. Use the work–energy principle to calculate its kinetic energy when it was at a height of 14 m above the ground. Take .
The driver of a car of mass 1,056 kg was approaching some traffic lights at 14 m/s. The lights turned red so he started braking to bring the car to a stop. The brakes applied a constant force of 128 kg-wt. Using the work-energy principle, determine the distance covered by the car until it came to rest. Consider the acceleration due to gravity to be 9.8 m/s2.
A body was at rest on a rough horizontal plane. A force of 10 kg-wt acted on the body causing its kinetic energy to increase to 57 kg-wt⋅m over a distance of 12 m. Using the work–energy principle, find the resistance of the plane to the body’s motion. Consider the acceleration due to gravity to be 9.8 m/s2.
A body of mass 15 kg started moving horizontally from a position of rest in a straight line under the action of a horizontal force of magnitude 250 g-wt. Given that it covered a distance of 6 m, use the work-energy principle to find its final speed. Take .
A body of mass 96 kg was moving in a straight line at 17 m/s. A force started acting on it in the opposite direction to its motion. As a result, over the next 96 m, its speed decreased to 11 m/s. Using the work-energy principle, determine the magnitude of the force.
A particle of mass 8 kg was left to descend along the line of greatest slope of a smooth plane inclined at to the horizontal. Using the work-energy principle, find the speed of the particle after it had moved a distance of 27 m down the slope, rounding your answer to two decimal places. Take .
A body of mass 400 g was placed at the top of an inclined plane of height 8.5 m. It descended the plane, and when it reached the bottom, its speed was 10 m/s. Using the work-energy principle, determine the magnitude of the work done by the resistance, given that it was constant throughout the movement. Take .
A body started moving from rest from the top of a ramp that is 312 cm long which was inclined at to the horizontal. When it reached the bottom, it continued moving on a horizontal plane. The resistance to the body’s motion is constant on both the ramp and the plane and equal to times the weight of the body. Determine the distance that the body covered on the horizontal plane until it came to rest.
A body of mass 70 kg was moving under the action of a force of 8 kg-wt acting parallel to its motion. After the body had moved under the action of the force for a distance of 200 cm, its kinetic energy became 1,851.5 million ergs. Using the work-energy principle, determine the speed of the body before the force started acting on it. Take .
A bullet of mass 57 g was moving at 224 m/s toward a thick wooden wall that was coated in a layer of rubber that was 4 cm thick. The bullet passed through the rubber and then embedded 6 cm into the wood before it stopped. If the resistance of the wood to the bullet's motion was constant and twice the resistance of the rubber, determine the resistance of the rubber and that of the wood using the principle of work and energy. Take .
A truck of mass 1.8 metric tons started moving from rest along a horizontal road against a resistance of 14 kg-wt per metric ton of its mass. After covering a distance of 250 m, its speed became 42 km/h. Using the work-energy principle, determine the force generated by the truck’s engine. Take .
A mechanical hammer of mass 0.9 metric tons fell vertically from a height of 3.6 m onto a pole of mass 450 kg. The hammer and the pole moved as one body, penetrating 10 cm into the ground. Using the work–energy principle, find the resistance of the ground to the motion of the pole in kilogram-weights. Take .
A cyclist was riding his bike along a straight horizontal road. After he had cycled 410 m under his own strength, the combined kinetic energy of the cyclist and his bike was 1,763 kg-wt⋅m. Then he stopped peddling. After the bike had covered another 240 m, the kinetic energy dropped to 827 kg-wt⋅m. Using the work-energy principle, determine the force generated by the cyclist and the resistance to the motion, assuming that both were constant. Take .
Two spheres of masses 110 g and 275 g were moving along the same straight line in the same direction at 55 cm/s and 90 cm/s, respectively. Given that they collided and coalesced into one body, find the loss of kinetic energy as a result of the impact.
A body of mass 9 kg was at rest on a rough horizontal plane. The resistance to the motion of the body was equal to its weight. A horizontal force of 25 kg-wt acted on the body for 3 seconds. As soon as the force stopped acting, the body collided with another body of mass 5 kg which had been at rest, and the two bodies coalesced into one body. Find the loss in kinetic energy as a result of the impact. Consider the acceleration due to gravity to be 9.8 m/s2.
Two spheres of masses 40 g and 10 g were moving in a straight line towards each other at 45 cm/s and 30 cm/s respectively. When the two spheres collided, they coalesced into one body. Determine the kinetic energy lost as a result of the impact in ergs.
A horizontal force of 6 kg-wt acted on a body of mass 28 kg for 5 seconds causing it to move from rest along a horizontal plane. At the end of this time interval, the force stopped acting and the body immediately collided with another body of mass 7 kg. They coalesced and moved as one body. Calculate the kinetic energy lost as a result of the impact. Take .
Two spheres and of masses 26 g and 12 g, respectively, were moving along a horizontal straight line in opposite directions. Sphere was moving at a constant speed of 10 cm/s, whereas sphere had an initial speed of 19 cm/s and was accelerating uniformly at 7 cm/s2. After sphere had covered a distance of 132 cm , the two spheres collided and coalesced into one body. Find the loss of kinetic energy due to the impact.
A bullet of mass 10 g was fired at 56,358 m/min at a target of mass 1 kg which was at rest. Given that the bullet lodged into the target and that they started to move backward as one body, determine their speed after the impact.
Two spheres were moving in opposite directions along a horizontal line. The first sphere had a mass of 6 kg, and its speed was 75 cm/s when it collided with the second sphere which was moving at 80 cm/s. As a result of the impact, the first sphere rebounded at 15 cm/s along the same line in the opposite direction, and the second sphere came to rest. Find the loss in kinetic energy as a result of the impact.