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

Answer:

6.57 m/s

Explanation:

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

W = $\int F dx = \frac{1}{2} m v^{2}- \frac{1}{2} m u^{2}$

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 =$\int_{1}^{1.5}(5.00N/m^{2})x^{2} cos 31 dx$

⇒ $(5)(0.866)[\frac{1.5^{3}}{3}-\frac{1^{3}}{3}]$ =3.39 J

$\frac{1}{2} m v^{2}- \frac{1}{2} m u^{2}$ = 3.39

⇒ $\frac{1}{2} (0.25) v^{2}- \frac{1}{2} (0.25)4^{2}$ = 3.30

⇒ Speed at x = 1.50 m = v = 6.57 m/s