Aim for FivePhysics 1

Translation between representations (TBR)

Cart oscillating on a spring

  • Unit 7
  • 12 points
  • About 28 minutes

You can use a calculator on this question, just like on exam day.

A multipart problem about one situation shown in several ways. You draw a diagram, derive equations, sketch or draw graphs, and then explain whether your answers agree with each other or use them to predict what happens when the situation changes. On the exam: Question 2 of 4. Section II has 4 questions in 95 minutes (50% of the exam score), one of each type in this order; calculator allowed. The CED suggests 25–30 minutes.

The question

A cart of mass m = 0.40 kg on a horizontal, frictionless track is attached to a horizontal spring with spring constant k = 40 N/m. The other end of the spring is fixed. The cart's position x is measured from the spring's equilibrium position, with positive to the right. The cart is pulled to x = −0.10 m and released from rest at time t = 0.

Suggested time: 28 minutes

Your answers are saved in this browser as you type.

Something wrong with this question?

What's wrong?

Please don't include personal details.

Part (a)

2 points

Describe the free-body diagram of the cart at the instant it is released. Then calculate the magnitude and direction of the cart's acceleration at that instant.

0 / 2,500 characters

Part (b)

3 points

Calculate the period of the oscillation, and write an equation for the cart's position x as a function of time t, with numerical values.

0 / 2,500 characters

Part (c)

2 points

Use energy conservation to calculate the cart's maximum speed.

0 / 2,500 characters

Part (d)

3 points

Describe the graphs of (i) position versus time and (ii) velocity versus time for one full period, starting at t = 0. Give the values and times of the maxima, minima, and zero crossings.

0 / 2,500 characters

Part (e)

2 points

Explain how your graphs in part (d) are consistent with (i) your energy calculation in part (c) and (ii) your free-body diagram and acceleration in part (a).

0 / 2,500 characters

Checking scoring…

Scoring it yourself shows you the rubric, examples and a model answer. Try writing your answer first.