Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

(III) Two drag forces act on a bicycle and rider: $F_{\mathrm{D} 1}$ due torolling resistance, which is essentially velocity independent;and $F_{\mathrm{D} 2}$ due to air resistance, which is proportional to $v^{2}$ .For a specific bike plus rider of total mass 78 $\mathrm{kg}$ ,$F_{\mathrm{D} 1} \approx 4.0 \mathrm{N}$ ; and for a speed of $2.2 \mathrm{m} / \mathrm{s}, F_{\mathrm{D} 2} \approx 1.0 \mathrm{N}$$$\begin{array}{c}{\text { (a) Show that the total drag force is }} \\ {F_{\mathrm{D}}=4.0+0.21 v^{2}}\end{array}$$where $v$ is in $\mathrm{m} / \mathrm{s},$ and $F_{\mathrm{D}}$ is in $\mathrm{N}$ and opposes the motion.$$\begin{array}{l}{\text { (b) Determine at what slope angle } \theta \text { the bike and rider can }} \\ {\text { coast downhill at a constant speed of } 8.0 \mathrm{m} / \mathrm{s} \text { . }}\end{array}$$

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

a. $\left(4.0+0.21 v^{2}\right) N$b. $1,c \quad 1^\circ 18^{\prime} 21.6^{\prime \prime}$

Physics 101 Mechanics

Chapter 5

Using Newton's Laws: Friction, Circular Motion, Drag Forces

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Rutgers, The State University of New Jersey

Simon Fraser University

McMaster University

Lectures

02:34

In physics, a rigid body is an object that is not deformed by the stress of external forces. The term "rigid body" is used in the context of classical mechanics, where it refers to a body that has no degrees of freedom and is completely described by its position and the forces applied to it. A rigid body is a special case of a solid body, and is one type of spatial body. The term "rigid body" is also used in the context of continuum mechanics, where it refers to a solid body that is deformed by external forces, but does not change in volume. In continuum mechanics, a rigid body is a continuous body that has no internal degrees of freedom. The term "rigid body" is also used in the context of quantum mechanics, where it refers to a body that cannot be squeezed into a smaller volume without changing its shape.

02:21

In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.

02:17

The resistance to motion o…

01:05

The main frictional force …

07:02

A bicyclist traveling with…

04:58

Cycling. For a touring bic…

08:57

00:59

A cyclist ridos along a ci…

00:45

When you ride a bicycle at…

01:50

01:10

05:05

A track consists of two ci…

01:46

so the rolling drag force is given by, if some capital D one, which is four Newtons. And also we know that the other, uh, drag force, which is essentially do you do a resistance is F off D, too, and that's given us be these quick. So that's velocity dependent. Now we can use the data to find bee or the proportion becomes constant and then add these to drag forces together to get the total that course. So first, if we want to find B, it's if r f sub d too divided by the square where d two is given as one Newton and the Square it is 2.2 media for seconds quit, so that gives us V as zero point toe CEO. 66 kg per meter. So that order drag course F off D is equal to if off f sub d one plus absolute D to which is for Newton's plus zero point to one. So we can write that roughly 0.21 kg for meter. So it's gonna be kg, um, be spread mu quints. So that's the total drag force that we have now in part B. Um we need to find out the angle of the downhill. So let's first draw the free body diagram off the bike and the writer, and then we can start from there. So let's say we have the bike around here and then we have the writer sitting on top of it. No, since the bike and the writer is going down here we have we can said the parallel slope parallel to the slope as positive X axis. If it's going downhill, then perpendicular and upward direction as positive y exes. No, we have mg, which is acting vertically downwards. Then we have the normal force, which is perpendicular toe the slope. We call it F off end. Then we have the drag force, which is acting in the opposite direction. You call it ever D. So in X direction, we can used Newton's second law in X and y direction. So in extraction, we have mg sine theta minus F D, which is equal do zero because, uh, the bicycle is coasting and at a constant speed. So there's no ax elation that's involved in, and we get em design, said I, due to the fact that this angers off the slow beast ADA. So using trick the angle between Y Axis and MD State as well. So the component off mg along y axis is mg cool science data and perpendicular to that is MG science data. Since it's going downwards, Onda, we consider downward direction is positive. So we have positive and decided that minus F d equals zero and again to repeat myself. Uh, we took zero because it's going down in with a constant speed. So from here we can actually write F D, which is equal to go. MG Science Data, or fada, is equal to sign in verse ft over mg now, given the numbers we can solve for it. So we have sign in verse. F D is for mutants plus 0.2066 kg for meter times velocity squared, which is eight meters per second squared there. Then mg is 78 kg times 9.8 meet over second squid, combining all of them together. We see that angle is 1.3 degree. Thank you

View More Answers From This Book

Find Another Textbook

Numerade Educator

01:58

If length time and energy are fundamental units then find the dimension of m…

07:41

A body of mass 500 gm is attached to a spring and the system is driven by an…

01:38

The ratio by mass of combining elements in aluminium fluoride is(a) 1:3 (b) …

01:14

A particle moves over three quarters of a circle of radius "r".Wha…

02:38

A body starting from rest covers a distance of 0.45km and acquires a velocit…

01:57

there are cars with masses 4kg and 10kg respectively that are at rest ka hav…

03:17

a bullet of mass 40kg traveling with a velocity of 18m/s penetrates a thin w…

02:04

CHECK THE CORRECTNESS OF THE EQUATION E=hv(frequency), where E IS THE ENERGY…

01:03

Find mass of the substance containing in a volume of 800cc whose sg is 0.75…

03:11

A body of mass 8kg at rest explodes into three parts whose masses are in the…