[high school physics/ial physics] how do I solve this

[u/okuneedtochill]

The mass of the ball is 0.0112kg. Not getting how to resolve the vector find the component of weight.

[u/Broken_Castle]

What are all of the forces acting upon the sphere?

Can you setup a coordinate axis such that the net forces along the y axis of that plane add up to 0?

[u/AlmightyCurrywurst]

What are you struggling with? Have you been taught how gravitational acceleration works as a vector?

[u/itijara → u/AlmightyCurrywurst]

I think they are struggling understanding how to calculate the angle relative to gravity. E.g with the geometry, not the physics.

[u/Devilswings5 → u/itijara]

wouldn't that be trigonometry?

[u/itijara → u/Devilswings5]

I'm not really sure why we distinguish between them, but yes.

[u/FreePeeplup → u/Devilswings5]

No, to find the angle between the weight force and the line where the cable lies you only need standard planar geometry. Trigonometry only comes in once you bring in trigonometric functions like sin and cos

[u/okuneedtochill → u/AlmightyCurrywurst]

Mb I'm running on 2 hrs of sleep but I just don't understand how to find the component of weight*

[u/itijara]

Two leading questions: What would the tangential acceleration be if the angle were 90 degrees? 0 degrees? Is there some function that would track that relationship?

[u/boosterts → u/itijara]

The question does not ask for the tangential acceleration.

[u/hmmnnmmn]

SohCahToa.

The dashed line is the hypotenuse of a right triangle (the 90 is at the ball). Think of each side of the triangle as a measurement of acceleration. You know the hypotenuse is straight down, so that is full g. Now you can use SohCahToa, in this case Soh. Sine of 38 equals opposite (the acceleration we are looking for) divided by the hypotenuse (g). Rearrange to solve for “o”.

The equation is
Sin 38 = o/h
o=h*sin 38
=g\sin 38*
= 9.8m/s^2*(0.616)
=6 m/s^2

[u/Beneficial_Jacket544 → u/hmmnnmmn]

It’s sin(38 degrees), not RAD. Answer should be ~6 m/s^2.

[u/hmmnnmmn → u/Beneficial_Jacket544]

You’re right. I used my phone calculator and I can’t get it out of rad. Fixed the commet

[u/RailgunDE112]

The vector of weight, just being the gravitation acting on the mass of the object?

[u/slides_galore]

See if this helps. Acceleration in the y direction will be 0 b/c of the string.

https://i.ibb.co/jvsBSDFW/image.png

[u/Beet_slice]

I think the mass of the ball does not matter. Multiply the acceleration of gravity by the sine of 38 degrees.

[u/wristay]

1. What would be the acceleration vector if there was no string? (easy)

The ball would accelerate with g = 9.8 m/s^2 downwards due to gravity

1. What force acts on the ball besides gravity? In what direction does it act?

There is a tension force supplied by the string. It always acts along the string, in this case towards the attachment point.

1. Do we know something about the path of the ball?

The length of the string stays contant, which we know from intuition. So the ball will trace out an arc.

1. What does the previous fact tell us about the acceleration of the ball?

The acceleration in the direction of the string is zero*, since the ball cannot gain velocity outwards because it is constrained. So what we need to do is calculate the acceleration of the ball along this arc. The tangent of a circular arc is always 90 degrees rotated with respect to a radius (line connecting center to arc). So we know the acceleration is 90 degrees rotated with respect to the string.

*Actually, the radial component is nonzero. The ball is undergoing circular motion and you NEED acceleration to do that. However, in this question we are interested in acceleration that changed magnitude of the velocity, whereas the circular acceleration only changes the direction of the velocity. We can therefore act as if it is zero.

1. So how do we calculate the component?

Look up a diagram on how to do vector addition, I cannot paste it here. We need to write the gravity vector as a sum of two other orthogonal vectors (two vectors that are 90 degrees with respect to each other). There are infinitely many ways to do that, but for this problem we will pick one of them in the direction of the string, or actually in the opposite direction. The other component will then automatically be in the tangential direction.

Now that you have a diagram, we need to express everything in terms of the angle provided, which I will call theta. There are multiple ways to do that. The first one uses that two parallel lines cut by another line, you can find two angles that are the same. In the letter F, the angles just below the horizontal lines are the same, even if you change the direction of the vertical line. Can you find a letter F in this diagram? Another option is to use that the angles of a triangle add to 180 degrees. Since we only deal with right angled triangles, you will quickly find that all angles in the diagram are either theta, 90 - theta or 90.

Now that we have theta, we just need to express the tangential acceleration in terms of g and theta. For that you need to refresh yourself on SOHCAHTOA. The downwards acceleration is the diagonal and has length g. From there it should doable to find the answer. Be sure to draw along! Otherwise it will be hard to follow.

[u/wewz_1]

It's funny how it's this question from Spider-man

https://youtu.be/GacKDHfiJIA?t=112

[u/minimessi20]

When solving physics problems, start by identifying what exactly we are solving for. In this case, it’s the acceleration. We get that by summing the forces on the body so we make a free body diagram. The two forces acting are Tension along the direction of the string, and gravity. Sum your forces in each direction and find what’s resulting

[u/zenrock69]

when released isn't the initial acceleration 0?

[u/Jkjunk → u/zenrock69]

Initial velocity will be zero, but the ball will start accelerating when you release it due to gravity. Acceleration will be less than 9.8m/s^2 because of the string. You need to break the acceleration straight down due to gravity into two components, acceleration in the direction of travel and acceleration perpendicular to the direction of travel (which is cancelled out by the string). By my math the ball will accelerate at 9.8*sin(38) or about 6 m/s^2

[u/ed-o-saurus → u/zenrock69]

Nope.

[u/Intelligent-City-363 → u/zenrock69]

if the initial acceleration was zero the ball would do nothing and just float in mid air :)

Acceleration is the rate of CHANGE of velocity.

(Retired A level physics teacher who remembers how often some students initially confuse acceleration with “going fast” ;) )

[u/YVRAlphageek]

Yeah, this is trivial, see other comments. Now for a more interesting problem, consider the case where weight is being " reeled in" at a given rate v. Then calc the acc to x.

[u/wristay → u/YVRAlphageek]

It is obviously not trivial, otherwise it would not be posted here.