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A solid homogenous sphere rolls without slipping down a plane that makes an angle of 30 degree with the horizontal find the linear acceleration of the sphere and the minimum coefficient of friction?
The linear acceleration of the sphere down the incline can be calculated using the formula (a = g \sin(\theta)), where (g) is the acceleration due to gravity (9.8 m/s(^2)) and (\theta) is the angle of the incline. Substituting the values, we get (a = 9.8 \times \sin(30) = 4.9 , \text{m/s}^2). The minimum coefficient of friction required to prevent slipping can be calculated using the formula (\mu_{\text{min}} = \tan(\theta)), where (\mu_{\text{min}}) is the minimum coefficient of static friction. Substituting the values, we get (\mu_{\text{min}} = \tan(30) \approx 0.577).
On a speed time graph the slope measurses acceleration?
If an object is allowed to free-fall under gravity, it will accelerate downwards at 9.8 metres per second per second (m s-2). This is equal to the standard gravity, symbol g, which on the surface of Earth has a value of around 9.8 newtons per kilogram (N kg-1) or 9.8 m s-2. Both units are equivalent.This is because the acceleration of an object is given by the net force that acts on it (in newtons) divided by its mass (in kilograms). This is Newton's second law:F = m aSo a = F / mIn the case of a free-falling object, the only force acting on the object is gravity, and the magnitude of this force is the mass of the object multiplied by standard gravity.F = m gSo the acceleration a = g, the standard gravity.On the other hand, consider an object at rest on a horizontal surface. The force of gravity still acts on the object, but it is being counteracted by an upward force provided by the surface, which is equal and opposite to the force of gravity.An object on a slope is somewhere between these two. Part of the force of gravity is counteracted by an upward force provided by the slope, but the remainder causes the object to accelerate down the slope (assuming the object is round or slippery). In fact we need to resolve the force into its components by using trigonometry.To answer the question, if the slope is at an angle theta (θ) to the horizontal, then the acceleration is given by:a = g sin(θ)If the slope is perfectly horizontal then θ = 0, and sin (0) = 0, so a = 0, and the object does not move.
Why ranges are equal at 30 degree and 60 degree?
this is due to effect of sin2(theta). as sin2(theta) will repeat its value for =90-theta as here theta=30 so for 90-30=60 sin2(30)=sin2(60) so for pair of projection angles of two projectiles as(theta,90-theta) , they will have same ranges i.e theta=10 and 90-10=80 sin2(10)=sin2(80)
Theta mode of replication in colE1 plasmid?
In the theta mode of replication in ColE1 plasmid, replication initiates from a single origin of replication called oriV. The replication machinery creates two replication forks that move in opposite directions around the circular DNA molecule, leading to the formation of two daughter plasmids. This mode of replication is common among small plasmids in bacteria and involves the formation of a theta structure resembling the Greek letter theta.
The gravitational acceleration on the surface of Mars is 3.7m s 2 What period Would a 64 meters long pendulum have on Mars?
The period of a pendulum on Mars compared to Earth would be about 1.62 times longer.The period of a pendulum is (among other factors) inversely proportional to the square root of the acceleration due to gravity. The gravity of Mars is 0.38 that of Earth, so the square root of one over 0.38 is 1.62.T ~= 2 pi sqrt (L/g) where theta far less than 1.For larger theta, longer periods are incurred, with various correction factors, but the basic equation remains the same.
Can sine theta equals to theta?
Yes, it can. If you plot theta and sin(theta) on the same graph, you will see where they intersect. I do not know of an analytical expression for this point; I think only numerical results are possible.
What is the relationship between g and acceleration of a pendulum?
The acceleration of a pendulum is directly proportional to the acceleration due to gravity (g). The formula to calculate the acceleration of a pendulum is a = g * sin(theta), where theta is the angle between the pendulum and the vertical line. This means that an increase in g will result in a corresponding increase in the acceleration of the pendulum.
Acceleration related to angle of inclination?
The acceleration of an object on an incline is influenced by the angle of inclination. A steeper incline will result in a greater component of the object's weight acting parallel to the incline, leading to a greater acceleration. The acceleration can be calculated using the formula a = g * sin(theta), where "a" is the acceleration, "g" is the acceleration due to gravity, and "theta" is the angle of inclination.
How do you graph a line using polar coordinates?
This only works for y=mx, not y=mx+c. theta = tan(m) eg y=x theta = tan(1) .: theta = 45
Use of an inclined plane in physics Hey guys I'm doing a prac investigation on an inlcined plane. I was wondering does mass affect acceleration down the incline?
inclined planes can be used in the investigation of acceleration. specificaly using m*g*sin(theta)=a (well i think that was the equation) acceleration is equal to mass*gravity*sin(theta) where sin(theta) is equal to opposite(o) over hypotenuse(h) or theta = (1/sin) * o/h
How does acceleration equal g sin theta?
I assume you are asking this in regards to an inclined plane so I will answer it accordingly, Well Recall the equation Force = Mass x Acceleration. In the case of free falling objects Acceleration is equal to gravity, however, on an inclined plan the presence of an incline prevents the object from falling straight down. Instead it must accelerate with some component of gravity. Now recall that perpendicular forces of action on an Incline plane are calculated by Sin theta and that perpendicular forces ( the normal force) is calculated by Cos theta Hence because the object is accelerating down an incline the formula for its total force parallel to the object would be Force = mg sin theta Now if you remember, if you simply remove the mass from the above equation you will be left with the acceleration component of the problem ala the force = mass x acceleration formula. So gsintheta represents A ( acceleration) in the Force = mass times acceleration formula.
Why does the acceleration of an object rolled down an incline increase as the angle of incline increases?
The contribution of the acceleration of gravity in the direction of motion increases as the angle of the incline increases. Or in other words, as the angle between the direction of motion and the force of gravity goes to zero, the acceleration of the object goes to the gravitational acceleration. a = g cos(theta) Where theta is the angle between the direction of motion and verticle, which is in fact (theta = 90 - angle of the incline)Where a is the acceleration of the object down the incline plane and g is the acceleration due to gravity. Theta is the angle between the direction of motion of the accelerating object and the acceleration of gravity. Initially, the angle between a and g is 90 degrees (no incline) and therefore g contributes nothing to the objects acceleration. a = g cos(90) = 0 As the angle of the inclined is increased, the angle between a and g approaches zero, at which point a = g. With no other forces acting upon the object, g is its maximum acceleration.
What is the equation for normal force?
The equation for normal force is: ( F_{\text{N}} = \text{mg} \cos(\theta) ), where ( F_{\text{N}} ) is the normal force, ( m ) is the mass of the object, ( g ) is the acceleration due to gravity, and ( \theta ) is the angle of incline.
How do you find theta?
You shoot a cannon with a vi of 18 m/s. You need to get it 16m and over a 10m wall. The acceleration in the x is 0 and in the y it is gravity. The question is at what angle theta can you shoot the cannon over the fence and 16 meters away. How do I find theta?
What is the eq of constant for a sphere rolling in a frictional less incline surface?
The equation for the constant acceleration of a sphere rolling without slipping on a frictionless inclined plane is given by a = g * sin(theta) / (1 + (I / (m * r^2))), where a is the acceleration, g is the acceleration due to gravity, theta is the angle of the incline, I is the moment of inertia of the sphere, m is the mass of the sphere, and r is the radius of the sphere.
What is the another word of heart-shaped?
I am assuming that you are talking about polar graphs. A limacon is a polar graph that has a heart shape. How much it looks like a heart depends on the type of limacon. There are looped, dimpled and convex. The equation of a limacon is r = b + a cos(theta) or r = b + a sin (theta). Theta is just the Greek letter theta that is the typical variable for an unknown angle.
Frictionless 30.0 incline What is the approximate magnitude of force f?
The magnitude of force f can be calculated using the equation f = mgsin(theta), where m is the mass of the object, g is the acceleration due to gravity, and theta is the angle of the incline. Given the angle of 30 degrees, the force can be calculated by plugging in the values of mass and acceleration due to gravity.
