1. 1 Find the mistakes in the following expressions and write the correct expressions:
( 1) r = x + y
Answer: r = xi+yj
(2) v = v x i + v y j
Answer: V = V X I+V Y J.
(3) v = v x i + v y j
Answer: V = V X I+V Y J.
(4) v = v x i + v y j
Answer: V = V X I+V Y J.
(5) v = (v 2
x + v
2
y
+ v 2
z)
1/2
Answer: v = (v 2
x + v
2
y
+ v 2
z)
1/2
1.2 known r = 2ti? 4t 2 j, 1 sec displacement δδr = 2i? 4j, the speed at any moment v(t) = 2i? 8tj, speed up
a(t) =？ 8j, the ballistic equation is y =? x 2
The kinematic equation of 1.3 flat projectile is x = 5t and y = 5t 2, then the potential vector r = 5t+5t 2j and the velocity v(t) = 5i+ 10tj at any moment.
The acceleration a(t) = 10j, and the orbital equation is x 2 = 5y.
1.4 the speed of a point moving in a straight line is v(t) = e? T, the initial position is x 0 = 2, then x(t) = 3? e？ t
Answer: x(t) = x 0+
t
e？ t dt = 2 +(？ e？ t)
t
= 2 + (? e？ t + 1)
1.5 throwing an object from the ground, its height h = 10t? 5t 2, the speed at any moment v(t) = 10? 10t, the time to reach the highest point.
Is t = 1.
Answer: physically? Degree, in the most? At point, the velocity of the object is zero v = dh/dt = 10? 10t = 0，t = 1。
Mathematical? Understanding degree, h(t) is a function of time, and the condition for this function to obtain the extreme value is dh/dt = 0. ..
1.6 to determine true or false:
(1) When an object moving in a straight line reaches the minimum speed, the acceleration must be zero; [? ]
(2) When the object moving in a straight line reaches the maximum position, the speed must be zero; [? ]
1.7 selection: if the potential vector of a particle is r, the velocity is v, the velocity is v, and the distance is s, then there must be b.
A.|δr | =δs =δr
B.|δr |？ =δs？ = δ r, when δ t→ 0, there is |dr| = ds? = dr
C.|δr |？ =δs？ = δ r, when δ t→ 0, there is | dr | =δr? = ds
D.|δr |？ =δs？ = δ r, when δ t→ 0, there is | dr | =δr = ds.
1.8 choice: according to the symbol of the above question, there must be C.
A.|v| = v，|v| = v B.|v|？ = v，|v|？ = v
C.|v| = v，|v|？ = v D.|v|？ = v，|v| = v
1.9 selection: the particle is located in the vector r = (x, y) at a certain moment, and the calculation error of its velocity v is a.
A. doctor; doctor
Trembling insanity (abbreviation for Delirium Tremens)
B.
Doctor; doctor
Trembling insanity (abbreviation for Delirium Tremens)
C. Repeat from the mark.
Trembling insanity (abbreviation for Delirium Tremens)
D.
√ (
Advanced (short for deluxe)
Trembling insanity (abbreviation for Delirium Tremens)
) 2
+
(dy
Trembling insanity (abbreviation for Delirium Tremens)
) 2
1. 10 The crane with a diameter of 40 cm is wound with thin steel wire rope, and the other end of the rope is hung with heavy objects. If a heavy object falls at some point,
When the acceleration is 1 m/s 2 and the speed is 0.3 m/s, the angular acceleration of the pulley is 5 rad/s 2 and the angular velocity is 1.5.
1
The answer to class exercises Chapter 65438 +0 particle mechanics
Radians per second
Solution: The falling distance of the object is equal to the rotating distance of the pulley edge, and the falling speed of the object is the linear speed of the pulley edge.
The speed is equal to the tangential acceleration of the pulley edge.
1. 1 1 There is a particle with a radius of 0. 1 m on the orbit, and its angular position θ = π+t 2, then the tangential acceleration at any time.
A t = 0.2, normal acceleration a n = 0.4t2.
Answer: ω =
dθ
Trembling insanity (abbreviation for Delirium Tremens)
= 2t，β =
dω
Trembling insanity (abbreviation for Delirium Tremens)
= 2,
a t = Rβ，a n = Rω 2
1. 12 There is a particle on the orbit with the radius of 1 m, and its distance s = 2t? 0.5t 2, tangent acceleration at any time.
a t =？ 1, normal acceleration a n = (2? t) 2
Answer: v =
Repeat from the mark.
Trembling insanity (abbreviation for Delirium Tremens)
= 2 ? t，
a t =
dv
Trembling insanity (abbreviation for Delirium Tremens)
= ? 1, an n =
v 2
rare
1. 13 to judge whether it is true or not:
(1) The circular motion with the center of the circle as the coordinate origin satisfies dr/dt = 0 and dr/dt? = 0; [? ]
(2) Uniform circular motion satisfies dv/dt = 0 and DV/DT = 0; ...........................................[×]
(3) Uniform curvilinear motion satisfies dv/dt = 0 and dv/dt? = 0; [? ]
(4) The function of normal acceleration is to change the direction of speed; [? ]
(5) The function of tangential acceleration is to change the speed; [? ]
(6) In circular motion, if a n is constant, a t is zero; [? ]
(7) In circular motion, if a t is a constant, an n is also a constant; ...............................................[×]
1. 14 when an object falls, it is subjected to gravity mg and air resistance f = kv, then the limit speed v T = mg/k, and if the resistance f = kv 2, then,
Limit speed v T =
√
Mg/kg
1. 15 to judge whether it is true or not:
(1) The greater the mass, the greater the inertia; [? ]
(2) The greater the speed of the object, the greater the inertia; .............................................................[×]
1. 16 choice: press an object on a rough vertical wall with horizontal force F N to keep it still. When F N increases gradually, the object will be damaged.
The magnitude of static friction.
A. it is not zero, but remains unchanged; B. increase in direct proportion to F N;
C. after reaching a certain maximum value, it remains unchanged;
1. 17 choice: for a section of expressway with a horizontal road surface, the trajectory radius of the turning point is r, and the friction coefficient between the automobile tire and the road surface is μ, so that the automobile will not
As for the occurrence of sideslip, where is the speed C of the car?
A. Not less than
√
μgR； B.it must be equal to
√
μgR；
C. at most
√
μgR； D. it is also necessary to determine the quality of the car m;
1. 18 selection: small objects slide down from a static state along a fixed arc-shaped smooth track. In the process of sliding down, b
A. Its acceleration direction always points to the center of the circle, and its speed is constant;
B. The supporting force of the crawler is increasing;
C. The magnitude of the resultant force it receives is changing, and the direction always points to the center of the circle;
D. The magnitude of the resultant force is constant and the speed is increasing;
1. 19 In the northeast coordinate system, car A moves eastward with v A = 2i m/s, and car B moves northward with VB = 3JM/s; Then the speed of b relative to a
Degree v BA = (3j? 2i) m/s
1.20 stable southerly wind speed v 1 = 2 m/s someone runs west at the speed of v2 = 4 m/s. What is the wind speed that this person feels?
√
2 2 + 4 2 =
√
20 m/s
The others are in the attachment.