contestada

You weigh 530 N. Your bathroom scale contains a light but very stiff ideal spring. When you stand at rest on the scale, the spring is compressed 1.80 cm. Your 180 N dog then gently jumps into your arms. How much work is done by the spring as the two of you are brought to rest by friction

Respuesta :

asuwafohjames

The work done by the spring is 14791.67.

To calculate the work done by the spring, first, we need to find the spring constant.

Formula:

  • F = ke................. Equation 1

Where:

  • F = Force on the spring
  • k = spring constant
  • e = compression.

Make k the subject of the equation

  • k = F/e................. Equation 2

From the question,

Given:

  • F = 530 N
  • e = 1.8 cm = 0.018 m

Substitute the given values into equation 2

  • k = 530/0.018
  • k = 29444.4 N/m.

When the dog jumps into the scale, the new compression is given

  • F' = ke'.............. Equation 1

Where:

  • F' = (530+180) = 710 N

Substitute into equation 3

  • e' = (710)/29444.4
  • e' = 0.024 m.

Finally, we use the formula to find the work done by the spring.

  • W = F'e'/2.................... Equation 3

Given:

  • F' = 710 N
  • e = 0.024 m

Substitute the values above into equation 4

  • W = 710(0.024)/2
  • W = 14791.67 J

Hence, the work done by the spring is 14791.67.

Learn more about work done here: https://brainly.com/question/18762601