A spring has a length of 0.313 m when a 0.300 kg mass hangs from it, and a lengt

Question

A spring has a length of 0.313 m when a 0.300 kg mass hangs from it, and a length of 0.750 m when a 2.92 kg mass hangs from it. What is the force constant of the spring? What is the unloaded length of the spring? Attach the same spring to a toy car and pull the car with the spring to make the toy car accelerate at a constant rate of 0.5 m/s^2 from the rest on a frictionless track. If the car's mass is 0.5 kg, what is the car's velocity after 3 second? How much work is done to the car by the spring?

Explanation / Answer

Let L is the original length of the spring.

m1 = 0.3 kg, m2 = 2.92 kg.

let x1 is the extension of the spring when m1 kg is hanged.

x1 = 0.313 - L

F1 = k*x1

m1*g = k*(0.313 - L) --------(1)

simillarly,

m2*q = k*(0.75 - L) --------(2)

m2*g - m1*g = k*(0.75 - L) - (0.313 - L)

(m2 - m1)*g = k*(0.75 - 0.313)

==> k = (m2 - m1)*g/(0.75 - 0.313)

= (2.92 - 0.3)*9.8/(0.75 - 0.313)

= 58.8 N/m

b) from equation 1

m1*g = k*(0.313 - L)

0.3*9.8 = 58.8*(0.313 - L)

0.3*9.8/58.8 = 0.313 - L

L = 0.313 - 0.3*9.8/58.8

= 0.263 m

c) let A is the amlitude,

F = k*A

m*a = k*A

A = m*a/k

= 0.5*0.5/58.8

= 0.00425 m

angular frequency of the motion,

w = sqrt(k/m)

= sqrt(58.8/0.5)

= 10.8 rad/s

use, x = A*cos(w*t)

v = -A*w*cos(w*t)

= -0.00425*10.8*cos(10.8*3)

= 0.025 m/s or 2.5 cm/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.