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# Newtonian Mechanics

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(Please use g = 9.8 m/s^2).

1) Three balls are launched at the same speed from a one-story building. Ball 1 is launched vertically up, ball 2 is launched horizontally, ball 3 is launched straight down. Which ball has the greatest speed as they hit the ground? There will be 40 more problems, to be solved using a calculator, with emphasis on oscillations, similar in style to the problems below. For these, solve to 3 significant figures, then insert the FIRST significant figure of your answer on the optical-scan answer sheet. For example, for 0.0486, the answer would be "4".

2) A 5-gram block is attached to a spring and moves with maximum speed 7.62 m/s and amplitude 4.56m. What is the period of the motion in seconds?

3) A 1.2-kg block attached to a spring (spring constant = 40N/m) moves in Simple Harmonic Motion (SHM) with amplitude = 2.34m. What is the (total) energy in joules? What is the maximum speed?

4) A harmonic oscillator operates at a frequency of 4.32 Hz and its maximum acceleration is 9.8 m/s2. Find the amplitude.

5) A 5-g block oscillates in SHM with maximum speed 0.567 m/s, while the maximum acceleration is 4.81 m/s2. What is the maximum displacement?

6) How high above the earth's surface would a projectile go when launched straight upwards at 4.65 km/s? Take the earth's radius = 6380 km and its mass = 5.98 X 10 kg.

7) A ball is thrown at a 45º angle with an initial speed of 60 m/s. neglecting air resistance, how high in meters with it be 3.0 s later? What is its speed at this time?

8) A 50-kg skier slides down a 10-degree incline with an acceleration of 1.2 m/s2. What is the strength of the frictional force acting on her (in Newtons)? What is the coefficient of friction?

9) A car traveling at 20 m/s turns a corner with a turn-radius of 60 meters. What is the magnitude of the car's acceleration during the turn, in m/s2? What is the car's angular velocity, in rad/s?

10) A = I + 2j - 3k and B = 6i - 2j + 4k. Find the z component of the B-2. Find the dot product of A and B.

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#### Solution Preview

Following is the text part of the solution. Please see the attached file for complete solution.

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(Please use g = 9.8 m/s^2).

1) Three balls are launched at the same speed from a one-story building. Ball 1 is launched vertically up, ball 2 is launched horizontally, ball 3 is launched straight down. Which ball has the greatest speed as they hit the ground?

They all have the same speed. One can prove this using conservation of energy.

Initial energy = ½ m u2 + mgh where h is the building height.
Final energy = ½ m v2

v = sqrt (u2 + 2gh)

2) A 5-gram block is attached to a spring and moves with maximum speed 7.62 m/s and amplitude 4.56m. What is the period of the motion in seconds?

Position of the block is given by x = A sin wt
Velocity = dx/dt = Aw cos wt.
Max velocity = Aw

Given that max velocity = 7.62 m/s and A = 4.56m

Aw = 7.62

w = 7.62/4.56 = 1.67 /s

Period T = 2 pi / w = 2 pi / 1.67 = 3.76 s

3) A 1.2-kg block attached to a spring (spring constant ...

#### Solution Summary

Ten questions have been answered. Questions involve a broad range of topics covered in Newtonian Mechanics. Excellent set of question for students who are looking to improve their proficiency in Physics.

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