In Lab 1, we used the equation a = 5/7g sin 0 for the theoretical acceleration for a frictionless ramp of a sphere is. Let's derive this equation. 1) Assume a ball starts from rest and goes down a frictionless ramp. Set the gravitational potential energy at the top to be equal to the translational plus rotational kinetic energy at the bottom of the ramp. Solve for velocity in terms of g and height h. 2) Now use a 1D kinematic equation to solve for the acceleration in terms of g, h, and the length of the ramp, Ax. 3) Now use trigonometry (SOHCAHTOA) to substitute h and Ax with the angle of the ramp from the ground, 0.
In Lab 1, we used the equation a = 5/7g sin 0 for the theoretical acceleration for a frictionless ramp of a sphere is. Let's derive this equation. 1) Assume a ball starts from rest and goes down a frictionless ramp. Set the gravitational potential energy at the top to be equal to the translational plus rotational kinetic energy at the bottom of the ramp. Solve for velocity in terms of g and height h. 2) Now use a 1D kinematic equation to solve for the acceleration in terms of g, h, and the length of the ramp, Ax. 3) Now use trigonometry (SOHCAHTOA) to substitute h and Ax with the angle of the ramp from the ground, 0.
In Lab 1, we used the equation a = 5/7g sin 0 for the theoretical acceleration for a frictionless ramp of a sphere is. Let's derive this equation. 1) Assume a ball starts from rest and goes down a frictionless ramp. Set the gravitational potential energy at the top to be equal to the translational plus rotational kinetic energy at the bottom of the ramp. Solve for velocity in terms of g and height h. 2) Now use a 1D kinematic equation to solve for the acceleration in terms of g, h, and the length of the ramp, Ax. 3) Now use trigonometry (SOHCAHTOA) to substitute h and Ax with the angle of the ramp from the ground, 0.
(If unable to complete all parts just let me know and I will repost it twice for part 2 & 3)
In Lab 1, we used the equation ? = 5/7? sin for the theoretical acceleration for a frictionless ramp of a sphere is. Let's derive this equation. 1) Assume a ball starts from rest and goes down a frictionless ramp. Set the gravitational potential energy at the top to be equal to the translational plus rotational kinetic energy at the bottom of the ramp. Solve for velocity in terms of g and height h. 2) Now use a 1D kinematic equation to solve for the acceleration in terms of g, h, and the length of the ramp, Δ?. 3) Now use trigonometry (SOHCAHTOA) to substitute h and Δ? with the angle of the ramp from the ground, ?.
Transcribed Image Text:Problem 1)
In Lab 1, we used the equation a = 5/7g sin 0 for the theoretical acceleration for a frictionless
ramp of a sphere is. Let's derive this equation.
1) Assume a ball starts from rest and goes down a frictionless ramp. Set the gravitational potential
energy at the top to be equal to the translational plus rotational kinetic energy at the bottom of
the ramp. Solve for velocity in terms of g and height h.
2) Now use a 1D kinematic equation to solve for the acceleration in terms of g, h, and the length
of the ramp, Ax.
3) Now use trigonometry (SOHCAHTOA) to substitute h and Ax with the angle of the ramp from
the ground, 0.
Study of objects in motion.
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