Answer:
The magnitude of the force acting on the sled is 60.5 newtons.
Explanation:
The Work-Energy Theorem states that the work done by the external force applied on the sled (
), in joules, is equal to the change of its translational kinetic energy (
), in joules:
(1)
By definitions of work and translational kinetic energy we expand the equation above:
(1b)
Where:
- External force applied on the sled, in newtons.
- Travelled distance, in meters.
- Initial and final velocities, in meters per second.
If we know that
,
,
and
, then the external force applied on the sled is:
![F = \frac{m\cdot (v_{2}^{2}-v_{1}^{2})}{2\cdot s}](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7Bm%5Ccdot%20%28v_%7B2%7D%5E%7B2%7D-v_%7B1%7D%5E%7B2%7D%29%7D%7B2%5Ccdot%20s%7D)
![F = \frac{(11\,kg)\cdot \left[\left(7\,\frac{m}{s} \right)^{2}-\left(4\,\frac{m}{s} \right)^{2}\right]}{2\cdot (3\,m)}](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7B%2811%5C%2Ckg%29%5Ccdot%20%5Cleft%5B%5Cleft%287%5C%2C%5Cfrac%7Bm%7D%7Bs%7D%20%5Cright%29%5E%7B2%7D-%5Cleft%284%5C%2C%5Cfrac%7Bm%7D%7Bs%7D%20%5Cright%29%5E%7B2%7D%5Cright%5D%7D%7B2%5Ccdot%20%283%5C%2Cm%29%7D)
![F = 60.5\,N](https://tex.z-dn.net/?f=F%20%3D%2060.5%5C%2CN)
The magnitude of the force acting on the sled is 60.5 newtons.