Answer:
2.55 m
Explanation:
Assuming the ball slides without rolling, there are two methods that can be used to find the displacement of the ball. Method 1 is to use the work-energy theorem, which says the work done on the ball is equal to the change in kinetic energy. Method 2 is to use Newton's second law of motion, which says the net force on an object is equal to its mass times acceleration, then use kinematics to solve for displacement.
Method 1: Work-energy theorem
W = ΔKE
Fd = KE − KE₀
-mgμ d = 0 − ½ mv₀²
gμ d = ½ v₀²
d = ½ v₀² / (gμ)
d = ½ (2.79 m/s)² / (9.8 m/s² × 0.156)
d = 2.55 m
Method 2: Newton's second law and kinematics
F = ma
-mgμ = ma
a = -gμ
a = -(9.8 m/s²) (0.156)
a = -1.53 m/s²
Given:
u = 2.79 m/s
v = 0 m/s
a = -1.53 m/s²
Find: s
v² = u² + 2as
(0 m/s)² = (2.79 m/s)² + 2 (-1.53 m/s²) s
s = 2.55 m
