Part A: You have a two-wheel trailer that you pull behind your ATV. Two children
ID: 2303378 • Letter: P
Question
Part A:
You have a two-wheel trailer that you pull behind your ATV. Two children with a combined mass of 80.2 kg hop on board for a ride through the woods and the springs (one for each wheel) each compress by 6.37 cm. When you pull the trailer over a tree root in the trail, it oscillates with a period of 2.14 s. Determine the following.
(a) force constant of the springs
N/m
(b) mass of the trailer
kg
(c) frequency of the oscillation
Hz
(d) time it takes for the trailer to bounce up and down 10 times
s
Part C: A 0.43-kg mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a compressed position. The record of time is started when the oscillating mass passes through the equilibrium position and the position of the mass at any time is shown in the drawing.
Determine the following.
(a) amplitude A of the motion
m
(b) angular frequency ?
rad/s
(c) spring constant k
N/m
(d) speed of the object at
t = 2.0 s
m/s
(e) magnitude of the object's acceleration at
t = 2.0 s
m/s2
Explanation / Answer
a)
K = m*g/2x= (80.2*9.8)/(2*0.0637) = 6169.23 N/m
b) K = M*W^2
M = K/W^2 = (6169.2308*2.14^2)/((2*3.14)^2) = 716.3731 kg
M = m+Mt
Mt = 636.1731 kg
c) f = 1/T = 1/2.14 = 0.4673 Hz
d) t = 10*(T) = 21.4 s
B) F = K*A = m*w^2*A = m*4*pi^2*f^2*A
f =u*m*g
u*m*g = m*4*pi^2*f^2*A^2
u = (4*3.14^2*1.37^2*4*10^-2)/(9.8) = 0.3021
C)
a) A = max point on y axis = 0.1 m
b) W = 2*pi/T = (2*31.4)/8 = 7.85 rad/s
c) K = m*W^2 = 0.43*7.85^2 = 26.4977 N/m
d) at t=2 the object is at extreme position
V = 0 m/s
e)
a = amax = A*W^2 = 6.1623 m/s^2