Chapter 5&6
Chapter 5&6
Chapter 5&6
∆p=m (V f– Vi)
Describe motion of a collection of objects; connect to Newton’s first and second laws.
Impulse
Impulse冲量: the change in momentum caused by the application of a force
over a time interval, (N•s); its direction is the same as the direction of the total
force on the object. 描述力在一定时间内,对物体状态产生了多少影响。
( )
Impulse is the time integration of force. The magnitude of an impulse can be found
by measuring the area under the force–time curve. 类比:s=v•∆t
注意三种计算方法。
Applications
10. A rubber ball with a mass of 0.25 kg is dropped from a height of 1.5 m onto the
floor. Just after bouncing from the floor, the ball has a velocity of 4.0 m/s [up].
(a) Determine the impulse imparted by the floor to the ball. Hint:能量守恒
(b) If the average force of the floor on the ball is 18 N [up], for how long is the ball
in contact with the floor?
8. A hockey player passes a puck that is initially at rest. The force exerted by the
stick on the puck is 1100.0 N [forward], and the stick is in contact with the puck for
5.0 ms.
(a) Determine the impulse imparted by the stick to the puck
(b) If the puck has a mass of 0.12 kg, calculate the speed of the puck just after it
leaves the hockey stick.
Applications
5.2 Conservation of Momentum in One Dimension
Law of Conservation of Momentum 动量守恒:
The collision in an isolated system does not change the total momentum of the
two objects. Whatever momentum is lost by one object in the collision is gained
by the other. The total momentum of the system is conserved.
根源:牛顿第三定理
Interactions within a system
1. Collision: two or more objects come together
2. Explosion: a single object or group of objects breaks apart
考虑几种特殊情况
1.When one mass is significantly greater than the other mass, and the larger mass
is stationary throughout the collision, Vf1≈ –Vi1, Vf2 ≈ Vi2 ≈ 0
2. m1=m2, 交换速度
Conservation of Mechanical Energy
During a head-on collision in one dimension, the kinetic energy of the moving
masses is converted into elastic potential energy, and then back into kinetic
energy during the rebound. Total mechanical energy is conserved throughout the
collision.
Objects+Spring: At maximum compression, the two objects must have the same
velocity, Vf.
Application
5. Dynamics cart 1 has a mass of 0.84 kg and is initially moving at 4.2 m/s [right].
Cart 1 undergoes an elastic head-on collision with dynamics cart 2. The mass of
cart 2 is 0.48 kg, and cart 2 is initially moving at 2.4 m/s [left]. The collision is
cushioned by a spring with spring constant 8000 N/m.
(a) Calculate the final velocity of each cart after they completely separate.
(b) Determine the compression of the spring during the collision at the moment
when cart 1 is moving at 3.0 m/s [right].
(c) Determine the maximum compression of the spring.
5.5 Collision in Two Dimensions
• Momentum is conserved for elastic and inelastic collisions.
注意:m这里指产生引力的物体的质量
Applications
7. Calculate the gravitational field strength of the Sun at a distance of 1.5•10^11 m
from its centre (Earth’s distance). Mass of the sun is 2.0 × 10^30 kg.
9. A 537 kg satellite orbits Earth with a speed of 4.3 km/s at a distance of 2.5•10^7
m from Earth’s centre. (a) Calculate the acceleration of the satellite. (b) Calculate
the gravitational force on the satellite. M earth is 2.0 × 10^30 kg.
6.2 Orbits
Satellites: 由于引力而围绕另一个物体旋转的物体
The speed of a satellite in uniform circular motion around a central body depends
on the mass of the central body, m, and the radius of the orbit, r:
For a given orbital radius, a satellite in circular orbit has a constant speed.
How to derive a satellite’s rotation speed ?
For a satellite in a circular orbit, the gravitational force provides the centripetal force.
The speed of a satellite depends on its orbital radius and is independent of the
satellite’s own mass. Its speed v must be constant.
Applications
1. Observations show matter at a distance of 5.34•10^17 m from the black hole
and travelling at speeds of 7.5•10^5 m/s. Calculate the mass of the black hole,
assuming the matter being observed moves in a circular orbit around it.
8. The region of the solar system between Mars and Jupiter, called the Asteroid
Belt, contains many asteroids that orbit the Sun. Consider an asteroid in a circular
orbit of radius 5.03•10^11 m. Mass of the sun is 1.99 × 10^30 kg.