# Newtonian Mechanics

(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.

© BrainMass Inc. brainmass.com October 16, 2018, 6:45 pm ad1c9bdddfhttps://brainmass.com/physics/energy/newtonian-mechanics-94049

#### Solution Preview

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

===================

(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.

Problem in Newtonian Mechanics

9)

The surfaces between a 6 kg block, the 24 kg wedge and between the 24 kg wedge and the horizontal plane are smooth (without fric-tion).

The acceleration of gravity is 9.8 m/s2 .

A block is released on the inclined plane (top side of the wedge).