1. How much work is required to stop an electron (m = 9.11 10^-31 kg) which is moving with a speed of 1.97 10^6 m/s?
2. An automobile is traveling along a highway at 91 km/h. If it travels instead at 100 km/h, what is the percent increase in the automobile's kinetic energy?
3. A baseball (m = 145 g) traveling 25 m/s moves a fielder's glove backward 25 cm when the ball is caught. What was the average force exerted by the ball on the glove?
4. At an accident scene on a level road, investigators measure a car's skid mark to be 58 m long. It was a rainy day and the coefficient of friction was estimated to be 0.36. Use these data to determine the speed of the car when the driver slammed on (and locked) the brakes.
5. A sled is initially given a shove up a frictionless 26.0° incline. It reaches a maximum vertical height 1.35 m higher than where it started. What was its initial speed?
6. In the high jump, the kinetic energy of an athlete is transformed into gravitational potential energy without the aid of a pole. With what minimum speed must the athlete leave the ground in order to lift his center of mass 1.95 m and cross the bar with a speed of 0.56 m/s?
1. To find the work required to stop an electron, we can use the work-energy principle. The work done on an object is equal to its change in kinetic energy. The initial kinetic energy of the electron is given by KE = (1/2)mv^2, where m is the mass of the electron and v is its velocity. Since the electron needs to be stopped, its final kinetic energy will be zero. Therefore, the work done to stop the electron is equal to its initial kinetic energy.
Work = KE = (1/2)mv^2
Plugging in the values, we get:
Work = (1/2)(9.11 * 10^-31 kg)(1.97 * 10^6 m/s)^2
2. To find the percent increase in an automobile's kinetic energy when its speed increases, we can use the equation for kinetic energy, KE = (1/2)mv^2. The kinetic energy is proportional to the square of the velocity.
Let KE1 be the initial kinetic energy when the automobile is traveling at 91 km/h, and KE2 be the final kinetic energy when it travels at 100 km/h.
Percent increase = [(KE2 - KE1) / KE1] * 100
3. To find the average force exerted by a baseball on a fielder's glove, we can use Newton's second law, which states that force is equal to mass times acceleration. In this case, the acceleration is the change in velocity over the time it takes to catch the ball.
The velocity of the ball changes from its initial velocity to zero when it is caught. The time it takes to catch the ball can be calculated using the distance traveled and the initial and final velocities.
Force = mass * acceleration
Acceleration = (final velocity - initial velocity) / time
4. To determine the speed of the car when the driver slammed on the brakes and locked them, we can use the equation for frictional force, which is equal to the coefficient of friction multiplied by the normal force on the car. The work done by the frictional force is equal to the change in kinetic energy of the car.
The distance the car skids, the coefficient of friction, and the mass of the car are given. By setting the work done by the frictional force equal to the change in kinetic energy, we can solve for the initial kinetic energy and then find the initial speed.
5. To find the initial speed of the sled, we can use the conservation of energy principle. At the top of the incline, the sled has the maximum potential energy and zero kinetic energy. At the bottom of the incline, it has the maximum kinetic energy and zero potential energy. Therefore, the change in potential energy is equal to the change in kinetic energy.
The change in potential energy is equal to the mass of the sled times the gravitational acceleration times the change in height. The change in kinetic energy is equal to (1/2)mv^2, where m is the mass of the sled and v is its initial velocity.
6. To find the minimum speed at which the athlete must leave the ground in order to lift his center of mass to a certain height and cross the bar with a certain velocity, we can use the conservation of energy principle.
At the maximum height, the gravitational potential energy of the athlete is the maximum, and the kinetic energy is zero. At the bar, the gravitational potential energy is zero, and the kinetic energy is (1/2)mv^2, where m is the mass of the athlete and v is the velocity at the bar.
The minimum speed needed to achieve this can be found by equating the initial gravitational potential energy to the final kinetic energy at the bar.