A magnetic field forces an electron to move in a circle with radial acceleration in a particular magnetic field. (a) What is the speed of the electron if the radius of its circular path is ? (b)What is the period of the motion?
a) Speed of the electron is .
b) Period of motion is.
1) Radial acceleration,
2) Radius of the circular path,
The centripetal acceleration of the object depends on the velocity and radius of the orbit. Using the equation of centripetal acceleration, we can calculate the speed of an electron moving in a circular direction. Using the value of the speed of an electron and the equation of period, we can find the period of motion of an electron.
From equation (i), we can write,
By rearranging this equation, we get,
Therefore, the speed of electron is .
From equation (ii), we can write
Substitute the value of given radius and speed calculated in part (a), we get
Therefore, the time period of rotation of electron is .
At one instant a bicyclist is due east of a park’s flagpole, going due south with a speed of . Then later, the cyclist is due north of the flagpole, going due east with a speed of .For the cyclist in this interval, what are the(a)magnitude and (b) direction of the displacement, the (c) magnitude and (d) direction of the average velocity and the (e) magnitude and (f) direction of the average acceleration?
Figure 4-53 shows the straight path of a particle across a x-y coordinate system as the particle is accelerated from rest during time interval . The acceleration is constant. The coordinates for point B are ; those for point are (a) What is the ratio of the acceleration components? (b) What are the coordinates of the particle if the motion is continued for another interval equal to ?
Suppose that a shot putter can put a shot at the world-class speed and at a height of. What horizontal distance would the shot travel if the launch angleis (a)and(b)? The answers indicate that the angle of, which maximizes the range of projectile motion, does not maximize the horizontal distance when the launch and landing are at different heights.
The pitcher in a slow-pitch softball game releases the ball at a point above ground level. A stroboscopic plot of the position of the ball is shown in Fig. 4-60, where the readings are apart and the ball is released at. (a) What is the initial speed of the ball? (b) What is the speed of the ball at the instant it reaches its maximum height above ground level? (c) What is that maximum height?
Curtain of death. A large metallic asteroid strikes Earth and quickly digs a crater into the rocky material below ground level by launching rocks upward and outward. The following table gives five pairs of launch speeds and angles (from the horizontal) for such rocks, based on a model of crater formation. (Other rocks, with intermediate speeds and angles, are also launched.) Suppose that you are at x=20 km when the asteroid strikes the ground at time t=0 nd position x=0 (Fig. 4-52). (a) At t=20 s , what are the x and y coordinates of the rocks headed in your direction from launches A through E? (b) Plot these coordinates and then sketch a curve through the points to include rocks with intermediate launch speeds and angles.The curve should indicate what you would see as you look up into the approaching rocks.
94% of StudySmarter users get better grades.Sign up for free