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Chapter 6: Problem 44

During an Olympic bobsled run, the Jamaican team makes a turn of radius \(7.6 \mathrm{~m}\) at a speed of \(96.6 \mathrm{~km} / \mathrm{h} .\) What is their acceleration in terms of \(g ?\)

Short Answer

Expert verified
The acceleration of the Jamaican bobsled team is approximately 3.2g.

Step by step solution

01

Convert Speed to Meters per Second

First, we need to convert the speed from kilometers per hour (km/h) to meters per second (m/s). The formula for conversion is: \(1 \text{ km/h} = \frac{1}{3.6} \text{ m/s}\). Thus, \(96.6 \text{ km/h} = \frac{96.6}{3.6} \text{ m/s}\).
02

Calculate the Centripetal Acceleration

The centripetal acceleration \(a_c\) is given by the formula \(a_c = \frac{v^2}{r}\), where \(v\) is the velocity in meters per second and \(r\) is the radius in meters. Use the converted speed from Step 1 and the given radius of \(7.6\) meters.
03

Express the Acceleration in Terms of g

To express the acceleration in terms of \(g\), divide the centripetal acceleration by \(9.8\,\text{m/s}^2\) (since \(1\,g = 9.8\,\text{m/s}^2\)). Thus, \(a_g = \frac{a_c}{9.8}\).
04

Final Calculation and Answer

Substitute the known values and perform the calculations to find the centripetal acceleration and then express it in terms of \(g\). Perform the division and round off to a sensible number of significant digits.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Physics Problem Solving
Physics problem-solving can seem daunting, but it becomes easier when broken down into logical steps. When tackling a problem, the first step is understanding what is being asked. In the given problem, we need to find the acceleration experienced by a bobsled team taking a turn, expressed in terms of gravity (g). This involves both converting units and applying the right formulas.
To solve physics problems:
  • Identify the quantities given in the problem and what you need to find.
  • Determine the necessary formulas, in this case, for centripetal acceleration and unit conversion.
  • Solve in steps to prevent mistakes, verifying units and calculations at each step.
Approaching problems with a clear method makes them more manageable and builds confidence in your physics skills.
Unit Conversion
Unit conversion is a crucial skill in physics, as different problems may present units in different scales. In our exercise, the speed was given in kilometers per hour (km/h) but needed to be converted to meters per second (m/s) for calculation purposes.
The conversion between these two units can be easily handled using the conversion factor:
  • 1 km/h = \(\frac{1}{3.6}\) m/s.
So to convert 96.6 km/h to m/s, you divide 96.6 by 3.6. This step ensures that all units are consistent with standard physics equations, such as those calculating acceleration or force. Remembering to double-check your converted values will help avoid errors in the remaining calculations.
Acceleration due to Gravity
Acceleration due to gravity, commonly denoted as \(g\), is a key concept in physics. It refers to the acceleration of an object caused by Earth's gravitational pull, which is approximately \(9.8 \, \text{m/s}^2\).In problems involving centripetal force or acceleration like this one, expressing results in terms of \(g\) can provide a better intuitive understanding of the magnitude of the forces involved.
To express an acceleration in terms of \(g\):
  • Calculate the actual acceleration (in this case, centripetal acceleration).
  • Divide this value by \(9.8 \, \text{m/s}^2\) to convert it to a multiple of \(g\).
This step is particularly useful because it gives a sense of how the calculated acceleration compares to the familiar acceleration due to gravity, aiding our grasp of the physical situation.

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Most popular questions from this chapter

Brake or turn? Figure 6-44 depicts an overhead view of a car's path as the car travels toward a wall. Assume that the driver begins to brake the car when the distance to the wall is \(d=107 \mathrm{~m},\) and take the car's mass as \(m=1400 \mathrm{~kg},\) its initial speed as \(v_{0}=35 \mathrm{~m} / \mathrm{s},\) and the coefficient of static friction as \(\mu_{s}=0.50 .\) Assume that the car's weight is distributed evenly on the four wheels, even during braking. (a) What magnitude of static friction is needed (between tires and road) to stop the car just as it reaches the wall? (b) What is the maximum possible static friction \(f_{s, \max } ?\) (c) If the coefficient of kinetic friction between the (sliding) tires and the road is \(\mu_{k}=0.40,\) at what speed will the car hit the wall? To avoid the crash, a driver could elect to turn the car so that it just barely misses the wall, as shown in the figure. (d) What magnitude of frictional force would be required to keep the car in a circular path of radius \(d\) and at the given speed \(v_{0}\), so that the car moves in a quarter circle and then parallel to the wall? (e) Is the required force less than \(f_{s, \max }\) so that a circular path is possible?

A baseball player with mass \(m=79 \mathrm{~kg},\) sliding into second base, is retarded by a frictional force of magnitude \(470 \mathrm{~N}\). What is the coefficient of kinetic friction \(\mu_{k}\) between the player and the ground?

A police officer in hot pursuit drives her car through a circular turn of radius \(300 \mathrm{~m}\) with a constant speed of \(80.0 \mathrm{~km} / \mathrm{h} .\) Her mass is \(55.0 \mathrm{~kg}\). What are (a) the magnitude and (b) the angle (relative to vertical) of the net force of the officer on the car seat? (Hint: Consider both horizontal and vertical forces.

Calculate the ratio of the drag force on a jet flying at \(1000 \mathrm{~km} / \mathrm{h}\) at an altitude of \(10 \mathrm{~km}\) to the drag force on a propdriven transport flying at half that speed and altitude. The density of air is \(0.38 \mathrm{~kg} / \mathrm{m}^{3}\) at \(10 \mathrm{~km}\) and \(0.67 \mathrm{~kg} / \mathrm{m}^{3}\) at \(5.0 \mathrm{~km} .\) Assume that the airplanes have the same effective cross-sectional area and drag coefficient \(C\).

Calculate the magnitude of the drag force on a missile \(53 \mathrm{~cm}\) in diameter cruising at \(250 \mathrm{~m} / \mathrm{s}\) at low altitude, where the density of air is \(1.2 \mathrm{~kg} / \mathrm{m}^{3} .\) Assume \(C=0.75\)
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