Question

A 325-N force accelerates a 50.0-kg crate from rest along a horizontal frictionless surface for a distance of 20.0 m as shown in the figure.

http://edugen.wileyplus.com/edugen/courses/crs3976/art/qb/qu/c06/r7-1.png

What is the final speed of the crate?

Answer 1

A 325-N force accelerates a 50.0-kg crate from rest along a horizontal frictionless surface for a distance of $20.0\mathrm{m}$ as shown in the figure.

http://edugen.wileyplus.com/edugen/courses/crs3976/art/qb/qu/c06/r7-1.png

What is the final speed of the crate?

The law of conservation of energy:

$$\Delta E + W = 0$$

where $\Delta E$ – change of body's energy, $W$ – work of force

Work for uniform force directed along displacement can be expressed by the following equation:

$$W = F d$$

where $F$ is the force, $d$ is the displacement.

Change of body's energy equals $-\frac{mv^2}{2}$, therefore:

$$\frac{mv^2}{2} = Fd$$ $$v = \sqrt{\frac{2Fd}{m}} = \sqrt{\frac{2 * 325 * 20}{50}} \frac{m}{s} = 16.1 \frac{m}{s}$$

Answer: $16.1 \frac{m}{s}$