Basic Spring Systems

Page Directions The numerical values in this worksheet are randomly generated allowing students the opportunity to conveniently practice, and drill, common situations.

Before beginning any given worksheet, please look over all of the questions and make sure that there are no duplicate answers shown for the same question. If duplicates are present simply refresh the page until every answer is unique.

In order to check an answer (even when you are just starting the worksheet on Question 1) it is necessary to omit

any questions that you have not answered. Once you start submitting answers, the page may be checked as many times as necesasary without changing the randomized answers. Relevant scoring will be provided at the top of the page only when you answer all of the questions on your original submission.

Directions: On this worksheet you will work with the basic relationships for spring systems.

omit

Question 1

The spring shown above is compressed by Dx from its equilibrium position. When released it launches a block across a frictionless surface with speed of 4 m/sec. The two springs in the following figure are identical to the spring shown above and are also compressed Dx to launch an identical block.

What is the block’s new speed as it passes through equilibrium?

2 m/sec0.18 m/sec8 m/sec5.7 m/sec

omit

Question 2 The two springs in the following figure are also identical to the initial spring in Question #1 but are compressed Dx equal to 2.4 times the original spring's compression.

If the same block is launched, what is its new speed as it passes through equilibrium?

2.8 m/sec2.0 m/sec4.4 m/sec6.8 m/sec

omit

Question 3

A spring is attached to a 2-kg block. The other end of the spring is pulled by a motorized toy train that moves forward at 7 cm/s. The spring constant is 88.7 N/m, and the coefficent of static friction between the block and the surface is µ_s = 0.50. The spring is at its equilibrium length at t = 0 seconds when the train starts to move. At what time does the block initially begin slipping?

1.58 x 10⁰ seconds1.1 x 10^-1 seconds9.8 x 10⁰ seconds7.73 x 10^-3 seconds

omit

Question 4

The air-track carts in the diagram shown above are sliding to the right at 2.4 m/sec. The spring between them has a spring constant of 88.7 N/m and is compressed 7 cm. At some point, the carts will slide past a flame that will burn through the string holding them together. If cart A has a mass of 400 grams and cart B has a mass of 200 grams, what would be the speed of cart B after the string is burned?

1.20 m/sec3.00 m/secthe correct answer is not provided0.60 m/sec3.60 m/sec

omit

Question 5 One end of a spring is attached to a wall while the other end reaches exactly to the edge of a frictionless table 1 meters tall. A block of mass 2.4 kg is pushed against the spring until it is compressed a distance of 4 cm. The block is released and is launched off the table, striking the ground 88.7 cm away from the table. Air resistance is negligible. What is the spring's force constant?

1.16 x 10⁴ N/m2.83 x 10⁴ N/m2.89 x 10³ N/m5.78 x 10³ N/m

omit

Question 6 What was the initial acceleration of the block in Question #5?

3.47 x 10³ m/sec²3.47 x 10⁵ m/sec²9.64 x 10¹ m/sec²9.64 x 10³ m/sec²