Ch. 05 - Using Newton's Laws: Friction, Circular Motion, Drag Forces

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 05 - Using Newton's Laws: Friction, Circular Motion, Drag Forces

Problem 16

Chapter 5, Problem 16

Police investigators, examining the scene of an accident involving a car and an old truck, measure 72-m-long skid marks for the truck, which nearly came to a stop before colliding with the car at rest. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of the truck assuming a level road.

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Identify the known values: The length of the skid marks is 72 m, the coefficient of kinetic friction (μ_k) is 0.80, and the truck comes to rest (final velocity v = 0 m/s). The goal is to find the initial speed of the truck (v₀). Assume the road is level, so the acceleration is due to friction only.

Use the work-energy principle or kinematic equations to relate the initial speed to the stopping distance. The work done by friction is equal to the change in kinetic energy: \( \frac{1}{2} m v_0^2 = f_k \cdot d \), where \( f_k \) is the force of kinetic friction and \( d \) is the stopping distance.

Express the force of kinetic friction \( f_k \) as \( f_k = \mu_k \cdot m \cdot g \), where \( m \) is the mass of the truck and \( g \) is the acceleration due to gravity (approximately 9.8 m/s²). Substitute this into the work-energy equation: \( \frac{1}{2} m v_0^2 = \mu_k \cdot m \cdot g \cdot d \).

Simplify the equation by canceling the mass \( m \) (since it appears on both sides) and solve for \( v_0 \): \( v_0 = \sqrt{2 \cdot \mu_k \cdot g \cdot d} \).

Substitute the known values: \( \mu_k = 0.80 \), \( g = 9.8 \ \text{m/s}^2 \), and \( d = 72 \ \text{m} \). This will give the initial speed of the truck. Perform the calculation to find the numerical result.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Kinetic Friction

Kinetic friction is the force that opposes the motion of two surfaces sliding past each other. It is quantified by the coefficient of kinetic friction, which is a dimensionless value representing the ratio of the frictional force to the normal force. In this scenario, the coefficient of kinetic friction between the truck's tires and the pavement is given as 0.80, indicating a relatively high level of friction that will affect the truck's deceleration as it skids.

Newton's Second Law of Motion

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This principle can be applied to determine the deceleration of the truck due to friction. By calculating the net force (frictional force) and knowing the mass of the truck, we can find the acceleration (or deceleration) experienced by the truck as it skids to a stop.

Kinematic Equations

Kinematic equations describe the motion of objects under constant acceleration. In this case, we can use the equation that relates initial velocity, final velocity, acceleration, and distance to estimate the truck's initial speed. Given that the truck nearly comes to a stop (final velocity is approximately zero) and the distance of the skid marks, we can rearrange the kinematic equation to solve for the initial speed before the truck began to skid.

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Related Practice

Textbook Question

Two blocks made of different materials connected together by a thin cord slide down a ramp inclined at an angle θ to the horizontal, Fig. 5–40 (block B is above block A). The masses of the blocks are m_A and m_B, and the coefficients of friction are μ_A and μ_B. If m_A = m_B=4.0kg, and μ_A = 0.20 and μ_B = 0.30, determine the acceleration of the blocks.

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Textbook Question

Suppose you are standing on a train accelerating at 0.20 g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to slide?

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Textbook Question

Show that if a skier moves at constant speed straight down a slope of angle θ (Example 5–6), then the coefficient of kinetic friction between skis and snow is μₖ = tanθ. Ignore air resistance.

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Textbook Question

Piles of snow on slippery roofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a slope of 24°. As the snow begins to melt, the coefficient of static friction decreases and the snow finally slips. Assuming that the distance from a chunk of snow to the edge of the roof is 6.0 m and the coefficient of kinetic friction is 0.20, calculate the speed of the snow chunk when it slides off the roof.

Textbook Question

A flatbed truck is carrying a heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?

Textbook Question

(II) How large must the coefficient of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95 km/h?

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