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Phys 101 LM2 learning object one

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Emma Piercey

This document contains three questions about horizontal mass-spring systems. Question 1 asks to calculate the spring constant k given the mass, displacement, and external force. Question 2 asks for the acceleration, angular frequency, frequency, and period of oscillation given the mass, displacement, and external force. Question 3 asks for the amplitude of motion and phase constant given the mass, spring constant, and initial displacement.

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Horizontal Mass-Spring Systems Worksheet Question 1: A mass of 1.5kg, at rest, is attached to a spring, which is attached to a wall 75.0cm away. An external force of 25.0N is required to compress the spring by 5.0cm. Assuming the surface beneath the mass is frictionless, what is the spring constant k? Question 2: A mass of 5.0kg, at rest on a frictionless surface, is attached to a spring, which is attached to a wall 50.0cm away. An external force of 30.0N is used to stretch the spring by 20.0cm. When the external force is removed: (A) What will the acceleration of the mass be? (B) What will the angular frequency, the frequency and the period of the objects motion be? Question 3: A mass of 3.0kg is at rest on a frictionless surface, attached to a spring with a spring constant of 26.0N/m. The spring is compressed by 30.0cm. When the mass is released: (A) What will the amplitude of the motion be? (B) What will the phase constant be?
Horizontal Mass-Spring Systems Worksheet (Solutions) Question 1: A mass of 1.5kg, at rest, is attached to a spring, which is attached to a wall 75.0cm away. An external force of 25.0N is required to compress the spring by 5.0cm. Assuming the surface beneath the mass is frictionless, what is the spring constant k? FNet = Fexternal + Fspring = 0 Fspring = -kx 0 = 25.0N + (-kx)= 25.0N k (0.05m) -25.0N/0.05m = - k 500N/m = k Question 2: A mass of 5.0kg, at rest on a frictionless surface, is attached to a spring, which is attached to a wall 50.0cm away. An external force of 30.0N is used to stretch the spring by 20.0cm. When the external force is removed: (A) What will the acceleration of the mass be? (B) What will the angular frequency, the frequency and the period of the objects motion be? (A) FNet = Fspring = ma (B) = (k/m) k = -30.0N/-0.200m = 150N/m Fspring = -Fexternal = ((150N/m)/(5.0kg)) = 30= 5.5 rad/s -30.0N = ma f = /(2) = (5.5rad/s)/(2) = 2.8/s -30.0N = (5.0kg)a T = 1/f = 1/(2.8/s) = 0.36s -30.0N/5.0kg = a -6.0m/s2 = a Question 3: A mass of 3.0kg is at rest on a frictionless surface, attached to a spring with a spring constant of 26.0N/m. The spring is compressed by 30.0cm. When the mass is released: (A) What will the amplitude of the motion be? (B) What will the phase constant be? (A) x(0)= Acos() v(0) = -Asin() [x(0)]2 = A2cos2() [v(0)]2 = 2A2sin2() (using trigonometric identity: 1 = cos2() +sin2()) 2A2 = 2A2sin2() + 2A2cos2() 2A2 = 2[x(0)]2 + [v(0)]2 A2 = [x(0)]2+ [v(0)]2/2 A = {[x(0)]2+[v(0)]2/2} = {[-0.300]2+ [0.0m/s]2/2} = 0.300m
(B)(using the trigonometric identity tan() = sin()/cos()) 2A2tan()= 2A2sin()/2A2 cos() tan()= [v(0)]/2[x(0)] = tan-1[(0.00m/s)/2(-0.300)] = 0

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Phys 101 LM2 learning object one

  • 1. Horizontal Mass-Spring Systems Worksheet Question 1: A mass of 1.5kg, at rest, is attached to a spring, which is attached to a wall 75.0cm away. An external force of 25.0N is required to compress the spring by 5.0cm. Assuming the surface beneath the mass is frictionless, what is the spring constant k? Question 2: A mass of 5.0kg, at rest on a frictionless surface, is attached to a spring, which is attached to a wall 50.0cm away. An external force of 30.0N is used to stretch the spring by 20.0cm. When the external force is removed: (A) What will the acceleration of the mass be? (B) What will the angular frequency, the frequency and the period of the objects motion be? Question 3: A mass of 3.0kg is at rest on a frictionless surface, attached to a spring with a spring constant of 26.0N/m. The spring is compressed by 30.0cm. When the mass is released: (A) What will the amplitude of the motion be? (B) What will the phase constant be?
  • 2. Horizontal Mass-Spring Systems Worksheet (Solutions) Question 1: A mass of 1.5kg, at rest, is attached to a spring, which is attached to a wall 75.0cm away. An external force of 25.0N is required to compress the spring by 5.0cm. Assuming the surface beneath the mass is frictionless, what is the spring constant k? FNet = Fexternal + Fspring = 0 Fspring = -kx 0 = 25.0N + (-kx)= 25.0N k (0.05m) -25.0N/0.05m = - k 500N/m = k Question 2: A mass of 5.0kg, at rest on a frictionless surface, is attached to a spring, which is attached to a wall 50.0cm away. An external force of 30.0N is used to stretch the spring by 20.0cm. When the external force is removed: (A) What will the acceleration of the mass be? (B) What will the angular frequency, the frequency and the period of the objects motion be? (A) FNet = Fspring = ma (B) = (k/m) k = -30.0N/-0.200m = 150N/m Fspring = -Fexternal = ((150N/m)/(5.0kg)) = 30= 5.5 rad/s -30.0N = ma f = /(2) = (5.5rad/s)/(2) = 2.8/s -30.0N = (5.0kg)a T = 1/f = 1/(2.8/s) = 0.36s -30.0N/5.0kg = a -6.0m/s2 = a Question 3: A mass of 3.0kg is at rest on a frictionless surface, attached to a spring with a spring constant of 26.0N/m. The spring is compressed by 30.0cm. When the mass is released: (A) What will the amplitude of the motion be? (B) What will the phase constant be? (A) x(0)= Acos() v(0) = -Asin() [x(0)]2 = A2cos2() [v(0)]2 = 2A2sin2() (using trigonometric identity: 1 = cos2() +sin2()) 2A2 = 2A2sin2() + 2A2cos2() 2A2 = 2[x(0)]2 + [v(0)]2 A2 = [x(0)]2+ [v(0)]2/2 A = {[x(0)]2+[v(0)]2/2} = {[-0.300]2+ [0.0m/s]2/2} = 0.300m
  • 3. (B)(using the trigonometric identity tan() = sin()/cos()) 2A2tan()= 2A2sin()/2A2 cos() tan()= [v(0)]/2[x(0)] = tan-1[(0.00m/s)/2(-0.300)] = 0