# Newton's Second Law of Motion and Gun Acceleration

Scientists are experimenting with a kind of gun that may eventually be used to fire payloads directly into orbit. In one test, this gun accelerates a 5.0-kg projectile from rest to a speed of 4.0 x 10^3 m/s^2. The net force accelerating the projectile is 4.9 x 10^5 N. How much time is required for the projectile to come up to speed?

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#### Solution Preview

Solution. Denote the net force accelerating the projectile by F, denote the acceleration of the projectile by a, ...

#### Solution Summary

The solution shows how to calculate the time needed to accelerate to certain speed by using Newton's second law.

23 problems on kinematics and Newton's motion laws

(See attached file for full problem description with diagrams)

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Question 1: A 0.20-kg billiard ball traveling at a speed of 15 m/s strikes the side rail of a pool table at an angle of 60 degree. If the ball rebounds at the same speed and angle, what is the change in its momentum?

Question 2: A one-dimensional impulse force acts on a 3.0-kg object, as described by the graph (see attachment). Find

(a) the magnitude of the impulse given to the object,

(b) the magnitude of the average force, and

(c) the final speed if the object had an initial speed of 6.0 m/s.

Question 3: A projectile that is fired from a gun has an initial velocity of 90.0 km/h at an angle of 60 degrees above the horizontal. When the projectile is at the top of its trajectory, an internal explosion causes it to separate into two fragments of equal mass. One of the fragments falls straight downward as though it had been released from rest. How far from the gun does the other fragment land?

Question 4: A ballistic pendulum is a device used to measure the velocity of a projectile - for example, the muzzle velocity of a rifle bullet. The projectile is shot horizontally into, and becomes embedded in, the bob of a pendulum. The pendulum swings upward to some height h, which is measured. The masses of the block and the bullet are known. Using the laws of momentum and energy, show that the initial velocity of the projectile is given by .

Question 5: For the apparatus pictured in the attachment, one ball swinging in at a speed of 2vo will not cause two balls to swing out with speeds vo. (a) Which law of physics precludes this situation from happening, the law of conservation of momentum or the law of conservation of mechanical energy? (b) Prove this law mathematically. [vo means v subscript o]

Question 6: Two balls with masses of 2.0 kg and 6.0 kg travel toward each other at speeds of 12 m/s and 4.0 m/s, respectively. If the balls have a head-on, inelastic collision and the 2.0-kg ball recoils with a speed of 8.0 m/s, how much kinetic energy is lost in the collision?

Question 7: Show that the fraction of kinetic energy lost in a ballistic-pendulum collision is equal to M / (m + M).

Question 8: Three particles, each with a mass of 0.25 kg, are located at ( - 4.0 m, 0), (2.0 m, 0), and (0, 3.0 m) and are acted on by forces (see attachment). Find the acceleration (magnitude and direction) of the center of mass of the system. [Hint: Consider the components of the acceleration.]

Question 9 : See attachment

Question 10 : See attachment

Question 11 : See attachment

Question 12: The force that a squirrel exerts on a nut it has found is observed over a 10 second interval, as shown on the graph (see attachment). What is the average power exerted by the squirrel.

A. 2.5W

B. 1.3W

C. 5.0W

D. 2.2W

E. Zero

Question 13 : See attachment

Question 14: A Stone is thrown horizontally with an initial speed of 7.5 m/s from the edge of the cliff. A stopwatch measures the stone trajectory from the top of the cliff to the bottom to be 2.5 s. What is the height of the cliff? ( Assume gravitational acceleration is 9.8 m/s^?

A. 31 m

B. 25 m

C. 19 m

D. 12 m

Question 15 : See attachment

Question 16: A car travels at 40 km/h for 30 minutes and 60 km/h for 15 minutes. How far does it travel in this time?

A. 45km

B. 37.5km

C. 35km

D. 28.4 km

E. 20km

Question 17: A 200-g mass attached to the end of a spring causes it to stretch 5.0 cm. If another 200-g mass is added to the spring, the potential energy of the spring will be________.

Question 17: A plane flying horizontally at a speed of 50 m/s and at an elevation drop of 160 m drops a package of supplies. Two seconds later it drops a second package. How far apart will the two packages land on the ground?

A. 283 m

B. 162 m

C. 100 m

D. 67.7 m

E. 177 m

Question 18: If you blow up a balloon, and then release it, the balloon will fly away as the air rushes out. This is an illustration of:

A. Newton's First Law

B. Newton's Third Law

C. Galileo's Law of Inertia

D. Newton's Second Law

Questions 19 - 23 : See attachment

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