Physics Calculation problems, for exam

[Ion1776]

Sorry I am new to the site and didnt follow the template, please don't delete this post, I need help with these problems.

1) A tightrope walker is practicing. She is balanced on a rope at the exact midpoint of the rope. The tension in the rope is 4000 N, and the mass of the tightrope walker is 64 kg. Consider the left side of the rope. What angle with the horizontal does it make? State this as a positive number in degrees.

2) Two people are pushing their stalled car up a hill with an incline of 3.40°. They are pushing parallel to the surface of the hill. The car's mass is 954 kg. What is the combined force they must apply to keep the car moving at a constant speed up the hill? Ignore the forces of friction and air resistance.

3) A block sits on an inclined plane, which is slowly being raised. The block remains motionless until the angle the plane makes with the horizontal is 22°. At this angle, the block begins to slide down the plane. What is the coefficient of static friction between the plane and the block?

4) A 0.0820 kg pair of fuzzy dice is attached to the rearview mirror of a car by a short string. The car accelerates at a constant rate, and the fuzzy dice hang at an angle due to the car's acceleration. If the dice hang at 9.50° from the vertical as the car accelerates, what is the acceleration of the car?

Help on any of these would be great and please include Answers, so i can work back through the problem and understand it

 

[Chewy0087]

in this forum we encourage people to have a go at the problems themselves then help them out when/if they get stuck, so show us what you've done/tried and we'll give you a hand however it's against the rules for us just to tell you the answers!

 

[Ion1776]

Alright ill type out what i got so far.

What funny is that my physics professor assign us all these problems to turn in, but he say there's no math on his exams, all concept

 

[Chewy0087]

well it's concept through math, wouldn't say it's not math =P, but yeah just bang down your working and if not me someone will check it for you and give you hints and tips

 

[Ion1776]

Well for

1. I drew a free body diagram, with the tightroper's weight as force down. Then the tension force on both sides of the rope as a force up, and to each side at an angle theta relative to horizontal.

Now I don't know what equations, or how to set up the mathematical part.

2. Drew a freebody diagram, then i drew the normal force perpendicular and up. Then i drew the weight directly down. Then i tried to draw their push force along the plane, upward. NOW i don't know how to balence the components of weight with normal force and push force.

3. need help getting started
4. need help getting started

 

[RoyalCat]

Well for

1. I drew a free body diagram, with the tightroper's weight as force down. Then the tension force on both sides of the rope as a force up, and to each side at an angle theta relative to horizontal.

Now I don't know what equations, or how to set up the mathematical part.

2. Drew a freebody diagram, then i drew the normal force perpendicular and up. Then i drew the weight directly down. Then i tried to draw their push force along the plane, upward. NOW i don't know how to balence the components of weight with normal force and push force.

3. need help getting started
4. need help getting started

All of these questions rely on one simple concept, equilibrium is defined by Newton's Second Law.

If the sum of all forces is 0 along a certain axis, then the mass is at rest along that axis (At rest means traveling at a constant velocity or at 0 velocity).

For each and every one of these problems, you need to draw a free body diagram, and get two equations based on Newton's Second Law out of them. One for some x axis, and another for some y axis. Some of the questions require another concept be applied.

The general scheme for static problems is something along these lines:
A free body diagram, with all the forces acting on the mass and some breakdown according to an x,y coordinate system (In questions dealing with rotation, you'll often find a radial/tangential breakdown of the forces more useful, but these are outside your scope at the moment).
NSL for the x axis:
$$\Sigma \vec F_x=0$$

NSL for the y axis:
$$\Sigma \vec F_y=0$$


1.
That's a good approach on the first question! Try and draw the rope as a free body. It is acted on by three forces, the weight of the tight-rope walker, and two tension forces, one at each of the anchor points. The tension forces act along the rope, that means that with respect to certain coordinate systems, they have two components, try and see what forces need to cancel each-other out.

2.
You're very very close. When a mass is traveling at a constant velocity along some axis, it is at rest with respect to that axis. Just look at the sum of forces along that axis, and think about what it is.

3.
Again, this is a question of breaking the forces acting on the block down into components perpendicular to the plane, and along the plane.
Consider the following:
On the verge of slipping, the force of static friction is at its maximum, $$f_s=f_s_{max}=\mu_s\cdot N$$

4.
Here you need to use Newton's second law once more, but now the following holds true instead:
$$\Sigma\vec F=m\vec a$$
Break the forces acting on the dice down into x and y components and see what Newton has to say about each axis.

 

[Ion1776]

I don't really understand the links. But what are the equations i should use for the problems, like how do i set it up, with the numbers and all

 

[Ion1776]

I figured out the first 3, Still can figure out number 4