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Physics
Principles of Physics for Scientists and Engineers
256 SOLVED PROBLEMS
Question: 20.5
An infinite sheet of charge is lying on the xy-plane as shown in Fig. 20.16. A positive charge is distributed uniformly over the plane of the sheet with a charge per unit area σ. Calculate the electric field at a point P located a distance a from the plane. ...
Verified Answer:
Let us divide the plane into narrow strips paralle...
Question: 3.3
The position of a particle moving along the x-axis varies with time t according to the relation x = t³ − 12 t + 20, where x is given in meters and t in seconds. (a) Find the velocity and the acceleration of the particle as a function of time. (b) Is there ever a time when v = 0? (c) Describe the ...
Verified Answer:
(a) To get the velocity v as a function of time t,...
Question: 3.4
A car accelerates uniformly from rest to a speed of 100 km/h in 18 s.(a) Find the acceleration of the car. (b) Find the distance that the car travels. (c) If the car brakes to a full stop over a distance of 100 m, then find its uniform deceleration. ...
Verified Answer:
(a) In this problem we are given
v_{o}[/lat...
Question: 3.5
In a cathode ray tube of a TV set, an electron with initial velocity vo = 2×10^4 m/s enters a region 2 cm long (see Fig. 3.11) where it is electrically accelerated in a straight line. The electron emerges from this region with a velocity v = 3×10^5 m/s. (a) What was its acceleration, assuming it ...
Verified Answer:
(a) Taking the motion to be along the x-axis, and ...
Question: 3.6
The remote-controlled truck shown in Fig. 3.12 moves along the x-axis with a constant acceleration of −2 m/s². As it passes the origin, i.e. xo = 0, its initial velocity is 14 m/s. (a) At what time t′ and position x′ does v′ = 0 (i.e. when the truck stops momentarily)? (b) At what times t1 and t2 ...
Verified Answer:
(a) Given
v_{o}
= 14 m/s, v′ = 0, a...
Question: 3.7
A ball is dropped from a tall building, as shown in Fig. 3.13. Choose the positive y to be downward with its origin at the top of the building, i.e. yo = 0. Find the following for the ball’s motion: (a) its acceleration, (b) the distance it falls in 2 s, (c) its velocity after falling 15 m, (d) the ...
Verified Answer:
(a) Since the positive y is downward, then the bal...
Question: 3.8
A boy throws a ball upwards, giving it an initial speed vo = 15 m/s. Neglect air resistance. (a) How long does the ball take to return to the boy’s hand? (b) What will be its velocity then? ...
Verified Answer:
(a) We choose the positive y upward with its origi...
Question: 3.9
A ball is thrown upward from the top of a building with an initial velocity vo = 20 m/s. The building is 40 m high and the ball just misses the edge of the building roof on its way down; see Fig. 3.15 and take g = 10 m/s². Neglecting air resistance, find: (a) the time t1 for the ball to reach its ...
Verified Answer:
(a) We choose upward as positive, i.e. a = −g = −1...
Question: 4.1
A particle moves over a path such that the components of its position with respect to an origin of coordinates are given as a function of time by: x = −t² + 12 t + 5 y = −2 t² + 16 t + 10 where t is in seconds and x and y are in meters. (a) Find the particle’s position vector r as a function of ...
Verified Answer:
(a) The position vector is given at time t by: [la...
Question: 23.4
The parallel plates in Fig. 23.9a have an area A = 0.2 m² and separation distance d = 0.01 m. The original potential difference between them is ΔVo = 300 V which decreases to ΔV = 100 V when a dielectric sheet fills the space between the plates, see Fig. 23.9b. (a) Calculate the capacitance Co, the ...
Verified Answer:
(a) Using the parallel-plate capacitor Eq. 23.5, w...
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