Answer:
s = t + 0.88 t²
Explanation:
According to Newton's second law of motion, the net force (∑F) on the crate is equal to its mass (m) times its acceleration (a). After finding the acceleration, we can use kinematic equations, also known as SUVAT equations, to model the crate's position as a function of time. Drawing a free-body diagram will allow us to show all the forces acting on the crate.
According to the free-body diagram, there are three forces on the crate:
- Normal force N pushing perpendicular to the inclined plane
- Friction force f pushing parallel to the inclined plane
- Weight force mg pulling down
Sum of forces in the parallel direction:
∑F = ma
mg sin θ − f = ma
a = g sin θ − f/m
a = g (h/L) − f/m
Plug in values and solve.
a = 9.8 m/s² (50 m / 250 m) − (20 N / 100 kg)
a = 1.76 m/s²
Next, use the kinematic equation:
s = ut + ½ at²
where
- s is the displacement
- u is the initial velocity
- a is the acceleration
- t is the time
Given u = 1 m/s and a = 1.76 m/s², the distance as a function of time is:
s = (1) t + ½ (1.76) t²
s = t + 0.88 t²
