#2 #6 #8 #14 #18 #20 #242. What is the kinetic energy of an 80-kg sprinter running at 10 m/s?
6. A 3-kg toy car with a speed of 3 m/s collides head-on with a 2-kg car travelling in the opposite direction with a speed of 2 m/s. If the cars are locked together after the collision, how much kinetic energy is lost?
The sketch below helps to clarify the situation in our minds.
Since we are asked to find the loss in kinetic energy which is the difference in the initial and final kinetic energies, we will need the initial kinetic energy. We are given everything to find this initial kinetic energy in the problem statement.
In order to find the final kinetic energy of the two toy cars stuck together, we need the final velocity which was not directly stated in the problem. We will find this by using conservation of momentum. The initial momentum can be determined with the given information.
We employ the principle of conservation of momentum to find the final velocity.
With the initial kinetic energy, the final mass of the two toy cars stuck together, and the final velocity in hand, we are now able to figure the change in the system's kinetic energy.
8. A 0.5-kg air-hockey puck is initially at rest. What will its kinetic energy be after a force of 0.4 N acts on it for a distance of 0.2 m?
The final kinetic energy of the air-hockey puck is the sum of the initial kinetic energy plus the kinetic energy gained via the work done on the puck. Here the initial kinetic energy is zero as the puck is initially at rest. Thus, the final kinetic energy is strictly from the work done by the 0.4 N force over the 20 cm distance.
14. How much work does a 70-kg person do against gravity in walking up a trail that gains 200 meters in elevation?
The work done is the force of gravity, that is the person's weight, times the change in height above the bottom of the trail.
18. If a 0.2-kg ball is dropped from a height of 5 meters, what is its kinetic energy when it hits the ground?
The kinetic energy gained is equal to the potential energy lost by the ball. This loss in potential energy is the weight of the ball times its original height above the ground.
20. How much kinetic energy must a high jumper with a mass of 70 kg generate in order to clear the bar at 2.1 meters? Assume that the jumper's center of mass is normally at 0.9 meters.
The amount of kinetic energy needed to get over the bar is the potential energy of the still high jumper 2.1 meters above the ground. Since the high jumper's center of mass is clearly not at the ground, but at a height 0.9 meters above the ground, a sketch is critical to obtaining the correct answer to this exercise.
From our sketch we see that the gain in height above the starting point will be 1.2 meters. Therefore, the kinetic energy needed is the potential energy gained during the 1.2 meter rise to get over the bar.
24. If a hair dryer is rated at 800 Watts, how much energy does it require in six minutes?
To solve this exercise we need to use the definition of power as the rate in which energy is converted from one form into another. In equation language this means that the power is the change in energy divided by the time. Note that a Watt is equal to a Joule per second, so we will need to convert the six minutes into seconds to get the answer.
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