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=10ms^-2).

• A. 150 ms^-2
• B. 1.5 ms^-2
• C. 50 ms^-2
• D. 1.2 ms^-2

Answer 1

The Correct Option is B

To solve this problem, we need to ensure that the force of static friction is equal to or greater than the force required to accelerate the body along with the car. Let's go through the steps:

1. Understand the concept of static friction:
   • Static friction is the force that must be overcome to start moving an object resting on a surface. The maximum static friction force is given by: \(F_{\text{max}} = \mu_s \cdot N\) where \(\mu_s\) is the coefficient of static friction, and \(N\) is the normal force.
2. Apply the problem's conditions:
   • The normal force \((N)\) on the body is equal to the weight of the body \((mg)\). Here, \(g = 10\, \text{m/s}^2\).
   • The force required to accelerate the body is \(F = ma\), where \(m\) is the mass of the body and \(a\) is the acceleration.
3. Use the equation for maximum static friction:
   • Set the maximum static friction equal to the force needed to move the body:
   • \(\mu_s \cdot mg = ma\)
   • By simplifying, we get the maximum possible acceleration: \(a = \mu_s \cdot g\)
4. Calculate using the provided values:
   • Substitute \(\mu_s = 0.15\) and \(g = 10\, \text{m/s}^2\) into the formula for maximum acceleration.
   • \(a = 0.15 \cdot 10 = 1.5\, \text{m/s}^2\)
5. Conclusion:
   • The maximum acceleration that allows the body to remain stationary relative to the car is \(1.5\, \text{m/s}^2\).
   • Therefore, the correct answer is 1.5 ms^-2.