Question

A force with magnitude (5.00N/m2)x2 and directed at a constant angle of 31.0◦ with the +x-axis acts on an object of mass 0.250 kg as the object moves parallel to the x-axis. There are no other forces on the object that have components parallel to the x-axis. How fast is the object moving at x = 1.50 m if it has a speed of 4.00 m/s at x = 1.00 m?

Answer 1

6.57 m/s

Step-by-step explanation:

From work energy theorem, work done = W = Change in Kinetic energy

W =
`\int F dx = (1)/(2) m v^(2)- (1)/(2) m u^(2)`

here v is the final velocity and u is the initial velocity and F is the force.

Horizontal component of the force is considered here since motion is along the horizontal (X) direction. So cos 31

Work done =
`\int_(1)^(1.5)(5.00N/m^(2))x^(2) cos 31 dx`

⇒
`(5)(0.866)[(1.5^(3))/(3)-(1^(3))/(3)]` =3.39 J

`(1)/(2) m v^(2)- (1)/(2) m u^(2)` = 3.39

⇒
`(1)/(2) (0.25) v^(2)- (1)/(2) (0.25)4^(2)` = 3.30

⇒ Speed at x = 1.50 m = v = 6.57 m/s