Reference no: EM13955862

1. A projectile of mass 0.6 kg is fired vertically upwards in the barrel of a gun by a vertical net propelling force of 50 N acting over a period of0.5 seconds.

Calculate:

(a) The velocity of the projectile when it leaves the gun.
(b) The height reached by the projectile.
(c) The time taken from the projectile leaving the gun to its return to the same height.

2. A flywheel (A) with a mass of 100 kg and radius of gyration 1200 mm rotates at 150 revs min-1 (clockwise). The kinetic energy of this flywheel is to be reduced by 20% by impacting it with a second flywheel (B) rotating at 80 revs min-1 in the opposite direction, such that they have the same (clockwise) angular velocity after impact.

（a）如果其回旋半径为800 mm，则计算所需的飞轮质量（b）。

（b）计算损失到周围环境的能量。

（c）冲击弹性吗？解释你的回答。

3. A container of mass 100 kg runs on overhead rails. The container is mounted on two wheels each having a mass of 15 kg, a diameter of 1.2 m and a radius of gyration of 0.4 m.

Calculate:

（a）在4 m s-1时行驶时车辆的总动能。

（b）使车辆在300毫米的距离内休息所需的弹簧刚度。

4. For a given spring-mass system, what would be the effect on ω of:

（a）增加质量的大小

(b) Increasing the amplitude of vibration

(c) Increasing the spring stiffness

(d) Increasing the phase lag.

5.附着在垂直弹簧的下端的质量使弹簧延伸25毫米至其平衡位置。然后，质量再移位20毫米并释放。进行振动和时间测量的痕迹。从这些测量值可以看出，当时间为0.05 s时，从平衡位置的位移为19.2 mm。

(a) Calculate the expected frequency of vibration.

（b）计算质量的最大加速度。

(c) Calculate the maximum velocity of the mass.

(d) Write the expression for the displacement of the mass as a function of time.

(e) Write the expression for the velocity of the mass as a function of time.

（f）编写质量加速度随时间的函数的表达式。