Answer:
79.7 m
Explanation:
The crate is pushed with an initial velocity, and is slowed down by friction. There are two methods that can be used to find the distance it travels. Method 1 is to use the work-energy theorem, which says the work done by friction equals the change in the crate's kinetic energy. Method 2 is to use Newton's second law of motion to find the rate of acceleration, then use kinematics to find the distance traveled.
Using Method 1, the initial kinetic energy equals the final kinetic energy plus the work done by friction:
KE₀ = KE + W
½ mv₀² = ½ mv² + mgμ d
½ v₀² = ½ v² + gμ d
gμ d = ½ (v₀² − v²)
d = ½ (v₀² − v²) / gμ
Plug in values:
d = ½ ((17.0 m/s)² − (0 m/s)²) / (9.8 m/s² × 0.185)
d = 79.7 m
Using Method 2, the net force on the crate is equal to the mass of the crate times its acceleration:
∑F = ma
-mgμ = ma
a = -gμ
a = -(9.8 m/s²) (0.185)
a = -1.813 m/s²
Using kinematic equation:
v² = v₀² + 2aΔx
Δx = (v² − v₀²) / 2a
Δx = ((0 m/s)² − (17.0 m/s)²) / 2(-1.813 m/s²)
Δx = 79.7 m
