How Large Must the Force Be to Keep the Crate Moving at Constant Speed?

Of course, you could do it the other way round, taking x and y components … then you'd have to say:"there is no acceleration in the y direction, so the sum of the components of force in that direction is zero …" :smile: I think you did this in your head, but it's easier to make a mistake if you do it in your head!
  • #1
HeavOnEarth
1
0

Homework Statement



A crate of books is to be put on a truck with
the help of some planks sloping up at 31◦. The
mass of the crate is 70 kg, and the coefficient
of sliding friction between it and the planks is
0.4. You and your friends push horizontally
with a force ~F .
The acceleration of gravity is 9.81 m/s2 .
Once the crate has started to move, how
large must F be in order to keep the crate
moving at constant speed? Answer in units of
kN.

Homework Equations


Fnet=ma
u*F= Ff

The Attempt at a Solution



i did .4 x F = sin(31) x 70 x 9.81, solving for F i get 884.192 N/ 1000
= .884192 kN
however it's wrong
so I am confused as how to approach this problem

i tried cos(31) as well
and I've tried these solutions; all of which were rejected ( on the UT website )
10/26/08 8:46 PM Try#1: .353677
10/26/08 9:46 PM Try#2: 141.471
10/26/08 9:46 PM Try#3: .141471
10/26/08 9:47 PM Try#4: .235447
10/26/08 9:48 PM Try#5: .884192
10/26/08 9:49 PM Try#6: 1.47154

also i apologize if i posted in the wrong forum/ had bad formatting

oh nevermind lovely physics forum~
i got the answer
for anyone who's interested here's the work process
(excuse my intangible markings i was doing this on another forum as well)

ma = Fpush - Fg - Ff
Ff = .4*(cos31)*686.7 = 235.4
Fg = 686.7*sin31 = 353.7
a = 0

0 = Fpush - 353.7 - 235.4
Fpush = 589.1 N

edit: Ah crap it's 9.81 ~_~
edit2: ah crap you're pushing horizontally

Fpush = Fhor - Ff
589.1 = Fhor*cos31 - .4*Fhor*sin31
589.1 = 0.651*Fhor

Fhor = 905 N
or .905 kNi would still appeiciate any form of physics whatsoever, tips and help drawing digrams, overall picture, mindset, some practice problems - recommend books/ websites
the main goal for me is to get a 4,5 on the AP physics C exam
 
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  • #2
Welcome to PF!

HeavOnEarth said:
i would still appeiciate any form of physics whatsoever, tips and help drawing digrams, overall picture, mindset, some practice problems - recommend books/ websites

Welcome to PF! :smile:

Tip: if you were systematic in writing the proof, you wouldn't have missed the F sin31º the first time.

You should always state which direction you're taking components in (and why) … don't just do it in your head, write it down …

in this case I can see that you took components in the normal direction, so you should have started by saying:

"there is no acceleration in the normal direction, so the sum of the components of force in that direction is zero … " :smile:
 
  • #3
next yearI would like to first commend you for attempting to solve this problem and seeking help when you encountered difficulties. This shows a strong dedication to understanding the concepts and applying them correctly.

In this problem, we are dealing with Newton's laws of motion and forces. The first thing to note is that the crate is at rest, so the net force on it is zero. This means that the forces pushing it (Fpush) must be equal to the forces acting against it (Fg and Ff). Fg is the force of gravity, which is equal to the mass of the crate (70 kg) multiplied by the acceleration of gravity (9.81 m/s^2). Ff is the force of friction, which is equal to the coefficient of sliding friction (0.4) multiplied by the normal force (the component of Fg that is perpendicular to the surface of the planks). In this case, the normal force is equal to Fg multiplied by the cosine of the angle of the planks (cos31).

To keep the crate moving at a constant speed, the force pushing it (Fpush) must be equal to the force of friction (Ff). This is because the crate is not accelerating, so the net force must be zero. Therefore, we can set up an equation:

Fpush = Ff
Fpush = 0.4 * (cos31) * (70 kg * 9.81 m/s^2)
Fpush = 235.4 N

However, this is the minimum force required to keep the crate moving at a constant speed. The question asks for the force in units of kN, so we need to convert 235.4 N to kN by dividing by 1000. This gives us a final answer of 0.2354 kN.

To improve your understanding and problem-solving skills, I recommend practicing more problems involving forces and Newton's laws. This will help you to become more familiar with the concepts and how to apply them correctly. You can also review your textbook or lecture notes for examples and explanations. Additionally, there are many online resources and practice problems available for free, such as Khan Academy or Physics Classroom. As for books, I would recommend "University Physics" by Young and Freedman or "Fundamentals of Physics" by Halliday, Resnick, and Walker. These are commonly used textbooks for introductory physics courses and have a lot of practice
 

Related to How Large Must the Force Be to Keep the Crate Moving at Constant Speed?

1. What are Newton's three laws of motion?

Newton's first law states that an object at rest will remain at rest and an object in motion will remain in motion at a constant velocity unless acted upon by an external force. 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. Newton's third law states that for every action, there is an equal and opposite reaction.

2. What is the relationship between force and acceleration?

According to Newton's second law, force and acceleration are directly proportional. This means that the greater the force applied to an object, the greater its acceleration will be. Similarly, the smaller the force applied, the smaller the acceleration will be. This relationship is described by the equation F=ma, where F is force, m is mass, and a is acceleration.

3. How does Newton's first law relate to everyday life?

Newton's first law, also known as the law of inertia, can be observed in everyday life. For example, when a car suddenly stops, the passengers are thrown forward because their bodies want to continue moving at the same velocity. This is an example of inertia, where an object in motion wants to stay in motion unless acted upon by an external force.

4. Can an object be at rest and in motion at the same time?

No, according to Newton's first law, an object can either be at rest or in motion, but not both at the same time. This is because an object's state of motion is defined as either moving at a constant velocity or at rest, and it will remain in that state unless acted upon by an external force.

5. How does Newton's third law apply to rocket propulsion?

Newton's third law states that for every action, there is an equal and opposite reaction. This can be observed in rocket propulsion, where the rocket's engine expels gas in one direction, causing an equal and opposite force in the opposite direction. This force propels the rocket forward, allowing it to overcome the force of gravity and travel into space.

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