Stopping distance and static friction

In summary, the problem involves a large box of mass M moving on a horizontal surface at speed v_0 with a small box of mass m on top. The coefficients of static and kinetic friction between the two boxes are μs and μk respectively. The task is to find an expression for the shortest distance dmin in which the large box can stop without the small box slipping, expressed in terms of v0, μs, and appropriate constants. To do this, we need to find the maximum deceleration that won't exceed the force due to static friction, which can be calculated using the equation F=μN. The final expression for dmin is -v_0^2 / 2(u_s/m), but it
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Homework Statement


A large box of mass M is moving on a horizontal surface at speed v_0. A small box of mass m sits on top of the large box. The coefficients of static and kinetic friction between the two boxes are μs and μk, respectively.
Find an expression for the shortest distance dmin in which the large box can stop without the small box slipping.
Express your answer in terms of the variables v0, μs, and appropriate constants.

Homework Equations


F=μN
a=F/m

delta S = -v_i^2 / (2a_s)= -v_0^2 / 2a_s

The Attempt at a Solution


Question asks for minimum stopping distance, delta s, I am looking for the max deceleration that won't have greater force than the force due to static friction, μN.

dmin = -v_0^2 / 2(u_s/m)
Is this correct?
thanks for any help
 
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Do the units match?
Without matching units it cannot be right.
 

1. What is stopping distance?

Stopping distance is the distance a moving object travels between the moment it starts to brake and the moment it comes to a complete stop. It is affected by various factors such as the speed of the object, the surface it is moving on, and the friction between the object and the surface.

2. How is stopping distance related to static friction?

Stopping distance is directly related to static friction. Static friction is the force that acts between two surfaces in contact and prevents them from sliding against each other. When an object is in motion, the force of static friction acts in the opposite direction of motion, eventually bringing the object to a stop. The greater the static friction, the shorter the stopping distance will be.

3. What is the role of the coefficient of friction in stopping distance?

The coefficient of friction is a measure of the amount of friction between two surfaces. It plays a crucial role in determining the stopping distance of an object. The higher the coefficient of friction, the greater the force of static friction, and thus the shorter the stopping distance will be.

4. How does speed affect stopping distance?

As an object's speed increases, its stopping distance also increases. This is because the force of static friction is directly proportional to the object's weight and the coefficient of friction, but it is also proportional to the speed squared. This means that a small increase in speed can result in a significant increase in stopping distance.

5. What are some ways to reduce stopping distance?

There are a few ways to reduce stopping distance, such as maintaining proper tire pressure, using high-quality tires with good tread, and driving at safe speeds. Additionally, increasing the coefficient of friction between the tires and the road surface, such as by using anti-lock brakes or traction control, can also help reduce stopping distance.

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