Calculate the maximum acceleration of a moving car so that a body lying on the floor of the car remains stationary. The coefficient of static friction between the body and the floor is 0.15 ( g = 10 m s–2). [2023]A: 1.2 m s–2 B: 150 m s–2 C: 1.5 m s–2 D: 50 m s–2
Question
Calculate the maximum acceleration of a moving car so that a body lying on the floor of the car remains stationary. The coefficient of static friction between the body and the floor is 0.15 ( g = 10 m s–2). [2023]A: 1.2 m s–2 B: 150 m s–2 C: 1.5 m s–2 D: 50 m s–2
Solution
The maximum acceleration of the car can be calculated using the formula for static friction, which is:
f = μN
where f is the force of friction, μ is the coefficient of static friction, and N is the normal force. In this case, the normal force is equal to the weight of the body, which is its mass times the acceleration due to gravity (g).
So, we can rewrite the equation as:
f = μmg
The force of friction is also equal to the mass of the body times its acceleration (a), so we can set these two equations equal to each other and solve for a:
ma = μmg
a = μg
Substituting the given values:
a = 0.15 * 10 m/s^2 = 1.5 m/s^2
So, the maximum acceleration of the car so that the body remains stationary is 1.5 m/s^2. The correct answer is C: 1.5 m/s^2.
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