Answer:
Magnitude of friction = 0.784 N
The direction = negative X direction.
Explanation:
Given that the acceleration is caused by a friction force. A counter attendant in a diner shoves a ketchup bottle with mass 0.20kg along a smooth, level lunch counter. The bottle leaves her hand with an initial velocity of 2.8m/s. As it slides, it slows down because of the horizontal friction force exerted on it by the countertop. The bottle slides a distance of 1.0m before coming to rest.
The given parameters are;
Mass m = 0.2 kg
Initial velocity U = 2.8 m/s
Distance S = 1.0 m
Let's first calculate the acceleration of the bottle as it slide by using the third equation of motion
V^2 = U^2 - 2as
As the bottle is going to rest, the final velocity V = 0
0 = 2.8^2 - 2 × a × 1
2a = 7.84
a = 7.84/2
a = 3.92 m/s^2
The frictional force F = ma
Substitute a and mass m into the formula
-F = 0.2 × 3.92
F = -784 N
Therefore, the magnitude of the frictional force is 784 N and the direction is in negative x direction.
