Net Force of an Object using position function and momentum principle

[leejqs]

Homework Statement

A 2.80 kilogram mass is moving in a plane, with its x and y coordinates given by x = 4.50t² - 1.15 and y = 2.90t³ + 1.95, where x and y are in meters and t is in seconds. Calculate the magnitude of the net force acting on this mass at t = 2.05 seconds

Homework Equations

Change in momentum (p) = F_net * Change in time

The Attempt at a Solution

In taking the derivatives of the y position and x position separately, I now have the velocity functions. When plugging in t=2.05 to these velocity functions, I found the y and x component velocities. By using the Pythagorean theorem, I found the magnitude of the velocity, then multiplied that magnitude by the mass, 2.8kg, to find the magnitude of the momentum of the object.

I have this momentum (114.7 N) equal to the net force times the time. However, when I divide 114N/2.05seconds, my answer of 55.9 N is not correct.

Any suggestions or hints would be greatly appreciated! Thanks!

 

[AvroArrow]

The force acting on the mass is given by the equation F = ma, where m is the mass and a is the acceleration. To find the acceleration, you need to take the second derivative of the position functions for x and y.For x: a_x = 9.00t - 1.15For y: a_y = 8.70t^2 + 1.95Now you can calculate the magnitude of the acceleration using the Pythagorean theorem:a = sqrt(a_x^2 + a_y^2) = 9.44 m/s^2Finally, you can calculate the magnitude of the net force:F = ma = (2.80 kg)(9.44 m/s^2) = 26.5 N