Question

A uniform, solid sphere of radius 3.75 cm and mass 4.00 kg starts with a purely translational speed of 1.75 m/s at the top of an inclined plane. The surface of the incline is 3.00 m long, and is tilted at an angle of 26.0∘ with respect to the horizontal. Assuming the sphere rolls without slipping down the incline, calculate the sphere's final translational speed ????2 at the bottom of the ramp.

Answer 1

Answer:

v_2=4.53m/s$v_2=4.53m/s$

Explanation:

In order to solve the exercise it is necessary to apply the energy conservation equation,

The equation says the following,

$mgdsin(\theta)+\frac{1}{2}mv^2_1=\frac{1}{2}mv^2_2+\frac{1}{2}Iw^2$

Replacing the formula for I of a sphere, we have

$mgdsin(\theta)+\frac{1}{2}mv^2_1=\frac{1}{2}mv^2_2+\frac{1}{2}\frac{2}{5}mr^2(\frac{v_2}{r})^2$

$mgdsin(\theta)+\frac{1}{2}mv^2_1=\frac{1}{2}mv^2_2+\frac{1}{5}mv^2_2=\frac{7}{10}mv^2_2$

$\frac{10}{7}gdsin(\theta)+\frac{5}{7}v^2_1=v^2_2$

In this way we get the expression

$v_2=\sqrt{\frac{10}{7}gdsin(\theta)+\frac{5}{7}v^2_1}$

We proceed to replace with the given values and obtain that

$v_2=\sqrt{\frac{10}{7}*9.8*3sin(26))+\frac{5}{7}*1.75^2}$

$v_2=4.53m/s$

Answer 2

v_2=4.53m/sv_2=4.53m/s

The equation says the following,

mgdsin(0) + 1/2mv2/1 = 1/2mv2/2 + 1/2Iw^2  

Replacing the formula for I of a sphere,

mgdsin(0) + 1/2mv2/1 = 1/2mv2/2 + 1/2 2/5mr^2 (v2/r)^2

mgdsin(0) + 1/2mv2/1 = 1/2mv2/2 + 1/5mv2/2 = 7/10mv2/2

10/7gdsin(0) + 5/7v2/1 = v2/2

In this way, we get the expression

v2 = sqrt(10/7gdsin(0) + 5/7v2/1)

v2 = sqrt(10/7 * 9.8 * 3sin(26)) + 5/7 * 1.75^2

v2 = 4.53m/s

Further Explanation  

The ball that rolls on the plane will experience two movements at once, namely the rotation of the axis of the ball and the translational field being traversed. Therefore, objects that do rolling motion have a rotational equation and a translational equation. The amount of kinetic energy possessed by the rolling body is the amount of rotational kinetic energy and translational kinetic energy. You will here learn about the ball rolling on a plane and incline.

An object can experience translational motion or rotational motion. Translational motion is the motion of objects whose direction is straight or curved. In translational motion using the concept of Newton II's law. While the rotational motion is the motion that has a rotation of a particular shaft. Rotational motion is caused by the torque, which is the tendency of a force to rotate a rigid body against a particular pivot point.

Learn More

Object Experience  https://brainly.com/question/13696852

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Details

Grade: College

Subject: Physics

Keyword: object, ball, roll