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Box Sliding Down Ramp

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Unit: Force and Newton's Laws

Prerequisites

Kinetic Friction

Later Topics

None

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Part 1

A box of mass m=43 kgm = 43\,\mathrm{kg} is unloaded from a moving van by sliding it down a ramp that has rollers (i.e., the ramp is approximately frictionless). The ramp is inclined at an angle θ=31∘\theta = 31^\circ to the horizontal and has a length L=13 mL = 13\,\mathrm{m}. In how much time will the box reach the bottom of the ramp? What will be its speed then?

Select the correct free-body diagram for the box as it slides down the ramp.

Correct!

Solution:

Solution

For a frictionless ramp, only two forces act on the box:

  1. Gravitational force F⃗g\vec{F}_g acts vertically downward.

  2. Normal force N⃗\vec{N} acts perpendicular to the ramp surface, pointing away from the incline.

Thus, the correct diagram has F⃗g\vec{F}_g pointing straight down (at 270∘270^\circ) and N⃗\vec{N} pointing perpendicular to the incline surface (at 90∘+θ90^\circ + \theta).

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