Question

question 1

the box that bob and jane are in ( total \\(m = 200\text{ kg}\\) ) is sitting precariously close to a ramp that leads down to the basement. just as jane finishes her sentence, the box is pushed and slides down the ramp! the box starts at the top of the frictionless ramp shown below with a velocity of \\(v_0 = 5.00\text{ m/s}\\).

how fast is the box moving at the bottom of the frictionless ramp in meters per second?

question 2

at the bottom of the ramp is a bit of floor where the coefficient of kinetic friction is \\(0.580\\). starting from the bottom of the ramp, what is the distance that the box travels before it comes to a stop?

Explanation:

Identify given parameters

We extract the physical values from the problem description and diagram:

• Total mass of the box, \(m = 200\text{ kg}\)
• Initial velocity at the top of the ramp, \(v_0 = 5.00\text{ m/s}\)
• Height of the frictionless ramp, \(h = 7\text{ m}\)
• Coefficient of kinetic friction on the flat floor, \(\mu_k = 0.580\)
• Acceleration due to gravity, \(g = 9.8\text{ m/s}^2\) (or \(9.81\text{ m/s}^2\))

Calculate velocity at the bottom of the ramp

Using the Conservation of Energy knowledge point

$$
LATEXBLOCK0
$$

Calculate stopping distance on the flat floor

Using the Work-Energy Theorem and Kinetic Friction knowledge points

$$
LATEXBLOCK1
$$

Answer:

Question 1

12.7

Question 2

14.3