# 4.6 Problem-solving strategies  (Page 4/4)

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A 1100-kg car pulls a boat on a trailer. (a) What total force resists the motion of the car, boat, and trailer, if the car exerts a 1900-N force on the road and produces an acceleration of $0\text{.}{\text{550 m/s}}^{2}$ ? The mass of the boat plus trailer is 700 kg. (b) What is the force in the hitch between the car and the trailer if 80% of the resisting forces are experienced by the boat and trailer?

(a) $\text{910 N}$

(b) $1\text{.}\text{11}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{N}$

(a) Find the magnitudes of the forces ${\mathbf{\text{F}}}_{1}$ and ${\mathbf{\text{F}}}_{2}$ that add to give the total force ${\mathbf{\text{F}}}_{\text{tot}}$ shown in [link] . This may be done either graphically or by using trigonometry. (b) Show graphically that the same total force is obtained independent of the order of addition of ${\mathbf{\text{F}}}_{1}$ and ${\mathbf{\text{F}}}_{2}$ . (c) Find the direction and magnitude of some other pair of vectors that add to give ${\mathbf{\text{F}}}_{\text{tot}}$ . Draw these to scale on the same drawing used in part (b) or a similar picture.

Two children pull a third child on a snow saucer sled exerting forces ${\mathbf{\text{F}}}_{1}$ and ${\mathbf{\text{F}}}_{2}$ as shown from above in [link] . Find the acceleration of the 49.00-kg sled and child system. Note that the direction of the frictional force is unspecified; it will be in the opposite direction of the sum of ${\mathbf{\text{F}}}_{1}$ and ${\mathbf{\text{F}}}_{2}$ .

$a=\text{0.139 m/s}$ , $\theta =12.4º$ north of east

Suppose your car was mired deeply in the mud and you wanted to use the method illustrated in [link] to pull it out. (a) What force would you have to exert perpendicular to the center of the rope to produce a force of 12,000 N on the car if the angle is 2.00°? In this part, explicitly show how you follow the steps in the Problem-Solving Strategy for Newton’s laws of motion. (b) Real ropes stretch under such forces. What force would be exerted on the car if the angle increases to 7.00° and you still apply the force found in part (a) to its center?

What force is exerted on the tooth in [link] if the tension in the wire is 25.0 N? Note that the force applied to the tooth is smaller than the tension in the wire, but this is necessitated by practical considerations of how force can be applied in the mouth. Explicitly show how you follow steps in the Problem-Solving Strategy for Newton’s laws of motion.

1. Use Newton’s laws since we are looking for forces.
2. Draw a free-body diagram:
3. The tension is given as $T=\text{25.0 N.}$ Find ${F}_{\text{app}}\text{.}$ Using Newton’s laws gives: ${\text{Σ F}}_{y}=0,$ so that applied force is due to the y -components of the two tensions: ${F}_{\text{app}}=2\phantom{\rule{0.25em}{0ex}}T\phantom{\rule{0.25em}{0ex}}\text{sin}\text{θ}=2\left(\text{25.0 N}\right)\text{sin}\left(\text{15º}\right)=\text{12.9 N}$

The x -components of the tension cancel. $\sum {F}_{x}=0$ .

4. This seems reasonable, since the applied tensions should be greater than the force applied to the tooth.

[link] shows Superhero and Trusty Sidekick hanging motionless from a rope. Superhero’s mass is 90.0 kg, while Trusty Sidekick’s is 55.0 kg, and the mass of the rope is negligible. (a) Draw a free-body diagram of the situation showing all forces acting on Superhero, Trusty Sidekick, and the rope. (b) Find the tension in the rope above Superhero. (c) Find the tension in the rope between Superhero and Trusty Sidekick. Indicate on your free-body diagram the system of interest used to solve each part.

A nurse pushes a cart by exerting a force on the handle at a downward angle $\text{35.0º}$ below the horizontal. The loaded cart has a mass of 28.0 kg, and the force of friction is 60.0 N. (a) Draw a free-body diagram for the system of interest. (b) What force must the nurse exert to move at a constant velocity?

Construct Your Own Problem Consider the tension in an elevator cable during the time the elevator starts from rest and accelerates its load upward to some cruising velocity. Taking the elevator and its load to be the system of interest, draw a free-body diagram. Then calculate the tension in the cable. Among the things to consider are the mass of the elevator and its load, the final velocity, and the time taken to reach that velocity.

Construct Your Own Problem Consider two people pushing a toboggan with four children on it up a snow-covered slope. Construct a problem in which you calculate the acceleration of the toboggan and its load. Include a free-body diagram of the appropriate system of interest as the basis for your analysis. Show vector forces and their components and explain the choice of coordinates. Among the things to be considered are the forces exerted by those pushing, the angle of the slope, and the masses of the toboggan and children.

Unreasonable Results (a) Repeat [link] , but assume an acceleration of $1\text{.}{\text{20 m/s}}^{2}$ is produced. (b) What is unreasonable about the result? (c) Which premise is unreasonable, and why is it unreasonable?

Unreasonable Results (a) What is the initial acceleration of a rocket that has a mass of $1\text{.}\text{50}×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\text{kg}$ at takeoff, the engines of which produce a thrust of $2\text{.}\text{00}×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\text{N}$ ? Do not neglect gravity. (b) What is unreasonable about the result? (This result has been unintentionally achieved by several real rockets.) (c) Which premise is unreasonable, or which premises are inconsistent? (You may find it useful to compare this problem to the rocket problem earlier in this section.)

Calculate the work done by an 85.0-kg man who pushes a crate 4.00 m up along a ramp that makes an angle of 20.0º20.0º with the horizontal. (See [link] .) He exerts a force of 500 N on the crate parallel to the ramp and moves at a constant speed. Be certain to include the work he does on the crate an
What is thermal heat all about
why uniform circular motion is called a periodic motion?.
when a train start from A & it returns at same station A . what is its acceleration?
what is distance of A to B of the stations and what is the time taken to reach B from A
BELLO
the information provided is not enough
aliyu
Hmmmm maybe the question is logical
yusuf
where are the parameters for calculation
HENRY
there is enough information to calculate an AVERAGE acceleration
Kwok
mistake, there is enough information to calculate an average velocity
Kwok
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Abel
what is the unit of momentum
Abel
wha are the types of radioactivity ?
what are the types of radioactivity
Worku
what is static friction
It is the opposite of kinetic friction
Mark
static fiction is friction between two surfaces in contact an none of sliding over on another, while Kinetic friction is friction between sliding surfaces in contact.
MINDERIUM
I don't get it,if it's static then there will be no friction.
author
It means that static friction is that friction that most be overcome before a body can move
kingsley
static friction is a force that keeps an object from moving, and it's the opposite of kinetic friction.
author
It is a force a body must overcome in order for the body to move.
Eboh
If a particle accelerator explodes what happens
Eboh
why we see the edge effect in case of the field lines of capacitor?
Arnab
what is wave
what is force
Muhammed
force is something which is responsible for the object to change its position
MINDERIUM
more technically it is the product of mass of an object and Acceleration produced in it
MINDERIUM
wave is disturbance in any medium
iqra
energy is distributed in any medium through particles of medium.
iqra
If a particle accelerator explodes what happens
we have to first figure out .... wats a particle accelerator first
Teh
What is surface tension
The resistive force of surface.
iqra
Who can tutor me on simple harmonic motion
on both a string and peldulum?
Anya
spring*
Anya
Yea
yusuf
Do you have a chit-chat contact
yusuf
I dont have social media but i do have an email?
Anya
Which is
yusuf
Where are you chatting from
yusuf
I don't understand the basics of this group
Jimmy
teach him SHM init
Anya
Simple harmonic motion
yusuf
how.an.equipotential.line is two dimension and equipotential surface is three dimension ?
definition of mass of conversion
Force equals mass time acceleration. Weight is a force and it can replace force in the equation. The acceleration would be gravity, which is an acceleration. To change from weight to mass divide by gravity (9.8 m/s^2).
Marisa
how many subject is in physics
the write question should be " How many Topics are in O- Level Physics, or other branches of physics.
effiom
how many topic are in physics
Praise
Praise what level are you
yusuf
If u are doing a levels in your first year you do AS topics therefore you do 5 big topic i.e particles radiation, waves and optics, mechanics,materials, electricity. After that you do A level topics like Specific Harmonic motion circular motion astrophysics depends really
Anya
Yeah basics of physics prin8
yusuf
Heat nd Co for a level
yusuf
yh I need someone to explain something im tryna solve . I'll send the question if u down for it
a ripple tank experiment a vibrating plane is used to generate wrinkles in the water .if the distance between two successive point is 3.5cm and the wave travel a distance of 31.5cm find the frequency of the vibration
Tamdy
hallow
Boniface
Boniface
the range of objects and phenomena studied in physics is
Boniface