# Car Deceleration Problem

A car is travelling at a steady speed of 90 km/h when an emergency occurs. The driver carries out a panic-braking stop, locking all the wheels (no ABS!).

a. Derive expressions for the deceleration under the following conditions:

i. if the car is ascending a slope of angle Q from the horizontal

ii. if it is on a horizontal road surface

iii. if it is descending the slope.

b. Assuming that the weather is dry, the slope is designated as 10% and the mass of the car, M, is 950 kg, determine for the three cases described in part (a) the decelerations and the time taken for the car to come to rest.

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#### Solution Preview

Thank you, for providing the friction factor. The solution of the problem is attached in a word file.

Car dynamics

Problem Statement

A car is travelling at a steady speed of 90 km h−1 when an emergency occurs. The driver carries out a panic-braking stop, locking all the wheels (no ABS!).

1. Derive expressions for the deceleration under the following conditions:

a. if the car is ascending a slope of angle Q from the horizontal

b. if it is on a horizontal road surface

c. if it is descending the slope.

2. Assuming that the weather is dry, the slope is designated as 10% and the mass of the car, M, is 950 kg, determine for the three cases described in part (a) the decelerations and the time taken for the car to come to rest.

Fundamentals Used

Force due to gravity: Force due to gravity always acts vertically down on any mass M. This force can be ...

#### Solution Summary

This solution helps with a car deceleration problem.

Five problems on velocity, acceleration, friction etc.

1)A coffee cup on the dashboard of a car slides forward on the dash when the driver decelerates from 42.7 km/hr to rest in 3.72s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?

2)A chain consisting of five links, each of mass 0.180 kg, is lifted vertically with a constant acceleration of a = 2.2 m/s2. Find the magnitude of the force that link 3 exerts on link 2. What is the magnitude of the force F that must be exerted on the top link to achieve this acceleration?

3)A railroad flatcar is loaded with crates. The coefficient of static friction between the crates and the floor is 0.26. If the train is moving at 58.1 km/hr, in how short a distance can the train be stopped with a constant acceleration without causing the crates to slide?

4)A block is at rest on an inclined plane whose elevation can be varied. The coefficient of static friction is µs= 0.44, and the coefficient of kinetic friction is µk = 0.15. The angle of elevation ? is increased slowly from the horizontal. At what value of ? does the block begin to slide (in degrees)? What is the acceleration of the block?

5)A block of mass 5.6 kg is pulled along a horizontal frictionless floor by a cord that exerts a force of 48.0 N at an angle 26.8° above the horizontal. What is the magnitude of the acceleration of the block? What is the magnitude of the normal force exerted on the mass by the floor?

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