College physics exercises - Education and Training Encyclopedia

College physics exercises

College physics (1) exercises.

Chapter 1 particle kinematics

1. When a particle moves in a general curve on a plane, its instantaneous velocity is instantaneous velocity v and its average velocity is average velocity. There must be the following relationship between them:

(1).

2. If the motion equation of a particle is x=6t-t2(SI), the displacement of the particle is, and the path of the particle is.

3. There is a particle moving in a straight line along the X axis, and the coordinate of time t is (SI). Try asking:

(1) second average speed; (2) the instantaneous speed at the end of the second second; (3) the distance of the second second.

4. The height of the lamp from the ground is h 1, and the height of people is h2. Under the light, it is moving at a constant speed along the V-shape.

Walking in a straight line horizontally, as shown in the figure, the shadow M of his head on the ground is along the ground.

Motion speed vM=.

5. The particle moves in a curve, the curve represents the position vector, S represents the distance, and at represents the tangential acceleration. In the following expression,

( 1) (2) (3) (4)

(a) Only (1) and (4) are correct; Only (2) and (4) are correct.

6. Which of the following statements is correct for an object moving along a curve?

(a) The tangential acceleration shall not be zero; (b) The normal acceleration shall not be zero (except at inflection points).

(c) Because the velocity is tangential, the normal component velocity must be zero, so the normal acceleration must be zero.

(d) If an object moves at a uniform speed, its total acceleration must be zero.

(e) If the acceleration of an object is a constant vector, it must move at a constant speed. [ ]

7. For a particle moving on a circle with radius r, the relationship between its speed and time is v=ct2(c is constant), then the path S (t) traveled by the particle from t=0 to t=; The tangential acceleration of the particle at time t =; The normal acceleration of a particle at time t an=.

Reference answer

1.(b) 2.8m, 10 m3. ( 1) (2) (3)

4.5.(D) 6。 (B) 7。

Chapter II Newton's Law of Motion

1. There is a particle with mass m moving along the positive direction of the X axis. Suppose the velocity of a particle passing through the coordinate X is kx(k is a natural number), the force acting on the particle at this time is f = _ _ _ _ _ _ _ and the time required for the particle to move from point X = x0 to point X = X 1? t=_____ .

2. A bullet with a mass of m horizontally shoots into the sand at a speed of v0. Assume that the resistance of the bullet is opposite to the speed, the size is proportional to the speed, and the proportional coefficient is k, ignoring the gravity of the bullet. Q:

(1) The function of the bullet's velocity changing with time after it is injected into sand;

(2) The maximum depth of the bullet entering the sand.

3. Under the action of centripetal force, the ball with mass m makes a circular motion with radius r and speed v in the horizontal plane, as shown in the figure. The ball moves counterclockwise from point A to the semicircle of point B, and the momentum increment should be

(A) (B)

As shown in the figure, water flows through a fixed turbine blade. The speed of water flowing through the front and rear curved surfaces of the blade is equal to V, and the mass of water flowing to the blade in unit time remains constant equal to Q, so the force and direction of water acting on the blade are.

5. Let F=6t+3(SI) act on an object with a mass of 1kg. If an object moves in a straight line from rest under the action of this force, the impulse of this force acting on the object within the time interval of 0 to 2.0s is I=.

6. There is a light spring with a stubborn coefficient of k and an original length of l0, which is hung on the ceiling. When balanced by hanging a tray at its lower end, its length becomes l 1. Then put a heavy object in the tray, and the length of the spring becomes l2. In the process of extending from l 1 to l2, the work done by elastic force is as follows.

(A) (B) (C) (D) [ ]

7. A particle moves in the positive direction of X axis under the action of force (SI). From x=0 to x=2m, the force and work are (a) 8j (b)12j (c)16j (d) 24j [].

8. A person carries water from a well with a depth of 10 meter. At the beginning, the bucket was filled with 10kg of water, and the mass of the bucket was 1kg. Due to water leakage in the bucket, the water leakage is 0.2kg per 1m elevation. The work done by people who require the bucket to be lifted from the well to the wellhead at a constant speed.

9. As shown in the figure, a particle in circular motion in the coordinate plane is subjected to a force. When the particle moves from the coordinate origin to the (0,2r) position, the work done by the force on it is

(A) (B)

(C)(D)ぅぅ

10. On a smooth horizontal desktop, lay a fixed semicircular barrier as shown in the figure. The slider with mass m enters the barrier in the tangential direction with initial velocity v0, and the friction coefficient between the slider and the barrier is? Try to prove that when the slider slides out from the other end of the barrier, the work done by friction is.

1 1. A force F acts on a particle with a mass of 1.0kg to make it move along the X axis. It is known that the equation of motion of a particle under this force is (SI). In the time interval from 0 to 4s: (1) the impulse of force f is I =；; (2) The work done by the force F to the particle W=.

12. Under the action of force (SI), a particle with mass m=2kg moves linearly along the positive direction of X axis from rest, and the work done by this force in the first three seconds is calculated.

13. Of the following statements, the correct one is

(a) The greater the impulse to particles, the greater the momentum;

(b) The impulse of action is equal to the impulse of reaction;

(d) When the momentum of an object changes, the kinetic energy of the object also changes. 〔〕

Reference answer

1.2., 3. (2)

4.5.6.(C) 7。 (A) 8。

9. 10。 (omitted)11.16n.s; 176J 12。 13. (2)

Chapter III Law of Conservation of Motion

1. The spring does not obey Hooke's law. If F is applied, the corresponding elongation is X, and the relationship between force and elongation is F=52.8x+38.4x2 (SI). Q:

(1) Work required by external force when the spring is stretched from fixed length x 1=0.50m to fixed length x2= 1.00m;

(2) Put the spring horizontally on a flat and smooth desktop, with one end fixed and the other end tied with an object with a mass of 2. 17kg, then stretch the spring to a certain length x2= 1.00m, and then release the object from the static state, so as to find the speed of the object when the spring returns to x 1=0.50m;

(3) Is the elasticity of this spring a conservative force?

2. The masses of the two particles are m 1, m2 respectively. When the distance between them is shortened from a to b, the work done by gravity is.

3. A meteorite fell to the ground from the height h above the ground, ignoring the air resistance. Q:

(1) What work did gravity do during the falling of the meteorite?

(2) How fast does the meteorite fall?

4. The following statements about the conservation conditions of mechanical energy and momentum are correct.

(a) Momentum and mechanical energy of a system that is not affected by external forces must be conserved at the same time;

(b) If the resultant force of external forces is zero and internal forces are conserved, the mechanical energy of the system will be conserved;

(d) If the work done by external force on a system is zero, the momentum and mechanical energy of the system must be conserved at the same time. [ ]

5. It is known that the mass of the earth is m, the mass of the sun is m, the distance from the center of the earth to the center of the sun is r, and the gravitational constant is g, then the orbital angular momentum of the earth moving around the sun is [].

(A) (B) (C) (D)

6. As shown in the figure, the X axis is in the horizontal direction and the Y axis is in the vertical direction. At time t=0, the particle with mass m is released from A and let it fall freely. Then at any time t, the moment to the origin o is =; At any time t, the angular momentum o = of the particle to the origin.

7. A particle with mass m moves along a spatial curve, and the motion equation of the curve in rectangular coordinate system is, where a, b,? Are constants, then the moment of this particle at the origin = _ _ _ _ _ _ _ _ _ _; The angular momentum of a particle to the origin is _ _ _ _ _.

8. On a smooth horizontal surface, there is a light spring with one end fixed and the other end connected with a slider with a mass of m= 1kg, as shown in the figure. The natural length of the spring l0=0.2m, and the stiffness coefficient k= 100N.m- 1. Let t=0, spring length l0 and slider speed v0=5m? S- 1, the direction is perpendicular to the spring. At a certain moment, the spring is located at the position perpendicular to the initial position, and the length L = 0.5m Find the magnitude and direction of the slider speed at this time.

Reference answer

1.( 1) (2) (3) is 2.

3.( 1) (2) 4.(C) 5。 (1)

6.7.0;

8. Angle between direction and spring length direction.

Chapter IV Fixed Axis Rotation of Rigid Body

1. There are two forces acting on a rigid body with a fixed axis of rotation:

(1) When these two forces act parallel to the axis, their combined torque to the axis must be zero;

(2) When these two forces act perpendicular to the axis, their combined torque to the axis may be zero;

(3) When the resultant force of these two forces is zero, their resultant moment to the shaft must also be zero;

(4) When the resultant moment of these two forces to the shaft is zero, their resultant force must also be zero.

In the above statement,

(a) Only (1) is correct. (B)( 1) and (2) are correct, while (3) and (4) are wrong.

(C)( 1), (2) and (3) are all right, and (4) is wrong. (D)( 1), (2), (3) and (4) are all correct. [ ]

2. Regarding the moment of inertia of a rigid body rotating around an axis, the following statement is correct.

(a) It only depends on the mass of the rigid body, and has nothing to do with the spatial distribution of the mass and the position of the axis.

(b) It depends on the mass of the rigid body and its spatial distribution, and has nothing to do with the position of the axis.

(d) It only depends on the position of the rotating shaft and has nothing to do with the mass of the rigid body and its spatial distribution. [ ]

3. A straight rod with a length of L and negligible mass, two ends of which are respectively fixed with 2m and m balls, and the rod can rotate around its center O in a vertical plane and perpendicular to the horizontal smooth fixed axis of the rod. At the beginning, the lever is at a certain angle with the horizontal direction and is in a static state, as shown in the figure. After releasing the lever, it rotates around the O axis. When the lever rotates to the horizontal position, the magnitude of resultant torque acting on the system is m = _ _ _ _ _ _ _, and what is the magnitude of angular acceleration of the system at this time? =________。

4. Wrap the string around the flywheel edge with a horizontal and smooth shaft. If a weight with mass m is hung at the end of the rope, the angular acceleration of the flywheel is 0. If the pulling force is 2mg instead of the thick rope, the angular acceleration of the flywheel is

(a) less than (b) greater than and less than 2

5. In order to find the moment of inertia of the flywheel with radius R=50cm to the fixed rotating shaft passing through its center and perpendicular to the disk surface, a thin rope is wound around the flywheel, and a heavy hammer with the mass of m 1=8kg is hung at the end of the rope, so that the heavy hammer falls from the height of 2m, and the falling time t 1= 16s is measured, and then another mass is used.

6. A disk with moment of inertia j rotates around a fixed axis with an initial angular velocity of. Let the resistance moment be proportional to the rotational angular velocity, that is, (k is a normal number), and find the time required for the angular velocity of the disk to change from zero to zero.

7. The radius of a pulley is 0.1m.. The moment of inertia relative to the central axis is 10-3kg? M2. A variable force F= 0.5t(SI) acts on the edge of the pulley in the tangential direction. If the pulley is initially stationary, ignore the friction of the bearing. Try to find its angular velocity at the end of1s.

8. The necessary and sufficient condition for the conservation of angular momentum of rigid body is

(a) Rigid bodies are not affected by external torque.

(b) The resultant torque on the rigid body is zero.

(d) The moment of inertia and angular velocity of the rigid body remain unchanged. [ ]

9. As shown in the figure, when a disk rotates around the horizontal axis O perpendicular to the disk surface, two bullets with the same mass, the same speed and opposite directions shoot into the disk and stay in the disk. At the moment after the bullet is fired, the angular velocity of the disk will be

(a) Large (b) Constant (c) Small (d) Uncertainty []

10. One flywheel rotates around the shaft at an angular velocity, and the moment of inertia of the flywheel to the shaft is: another stationary flywheel suddenly engages with the same shaft, and its moment of inertia to the shaft is twice that of the former. Angular velocity of the whole system after meshing _ _ _ _ _ _ _ _.

1 1. As shown in the figure, a homogeneous wooden ball is fixed at the lower end of a thin rod and can rotate around a smooth axis O fixed horizontally .. Today, a bullet hits a wooden ball at a certain angle with the horizontal plane and is embedded in it. In this striking process, _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

12. As shown in the figure, a uniform thin rod with length L and mass M is freely suspended on a horizontal smooth shaft O passing through its upper end, and the moment of inertia of the rod to the shaft is 0. At present, a bullet with a mass of m hits the rod at a distance from the O-axis at a horizontal speed, and the maximum deflection angle of the rod is _ _ _ _ _ _ _.

13. A cylinder with mass m = 15 kg and radius r = 0.30 m can rotate around a horizontal fixed axis coincident with its geometric axis (moment of inertia). At present, an inextensible light rope is wound around the cylinder, and there is no relative sliding between the rope and the cylinder. An object with a mass of m = 8.0 kg is suspended at the lower end of the rope. Regardless of the friction between the cylinder and the shaft.

(1) Draw and display the chart;

(2) The distance of the object falling from rest within 2)5s;

(3) the tension of the rope.

14. As shown in the figure, an object with a mass of m is similar to the objects around the crown block.

The rope is connected together, the quality of the rope can be ignored, and there is no relative sliding between it and the crown block. Wrong setting slip.

The wheel mass is m, the radius is r, the moment of inertia is 0, and the pulley shaft is smooth. Try to find that object.

The relationship between falling speed and time during falling from rest.

Reference answer

1.(B) 2。 3. mg l/2.2g /(3 l) 4. (C) 5。 6.7.8.(B) 9。 (C) 10。

1 1. 12.

13.

Solution: (1) graph

=0.675 kg？ The second part of money supply

mg–T = ma

TR = J？

a = R？

The solution is = 5.06m /S2.