Two identical steel balls, each of mass 67.8 g, are moving in opposite directions at 4.80 m/s. They collide head-on and bounce apart elastically. By squeezing one of the balls in a vise while precise measurements are made of the resulting amount of compression, you find that Hooke's law is a good model of the ball's elastic behavior. A force of 15.9 kN exerted by each jaw of the vise reduces the diameter by 0.130 mm. Model the motion of each ball, while the balls are in contact, as one-half of a cycle of simple harmonic motion. Compute the time interval for which the balls are in contact.

Explanation:

To detrmine the time interval at which the balls are in contact.

Given information

The mass of each steal ball 67.8g. The speed of ball towards each other is 4.80 m/s. The exerted force by each jaw 15.9 kN and the forece reduce the diameter by 0.130 mm.

Expression for the effective spring constant ball is shown below.

K = |F|/|x|

Here,

k is a spring constant

F is the force exerted on the ball

x is dispalcement due force

substitute 15.9 kN for F and 0.130 mm in above equation

The spring constant is 122 x 10⁶ N/m

not too sure thinking it will always be directed towards the centre of the earth. could be wrong not sure

  distance on the y-axis and time on the x-axis.

explanation:

the instantaneous velocity = change in position/time taken

the slope of the graph should give instantaneous velocity.

  slope of a graph = change in value of y -axis / change in values of x -axis

  comparing both the equations

    change in value of y -axis = change in position

  change in values of x -axis = time taken

so position values should be on the y axis and time values should be on the x axis.

distance on the y-axis and time on the x-axis.