SSM A massless rigid rod of length L has a ball of mass m attached to one end (Fig. 8-68). The other end is pivoted in such a way that the ball will move in a vertical circle. First, assume that there is no friction at the pivot. The system is launched downward from the horizontal position A with initial speed v 0 . The ball just barely reaches point D and then stops. (a) Derive an expression for v 0 in terms of L, m , and g. (b) What is the tension in the rod when the ball passes through B ? (c) A little grit is placed on the pivot to increase the friction there. Then the ball just barely reaches C when launched from A with the same speed as before. What is the decrease in the mechanical energy during this motion? (d) What is the decrease in the mechanical energy by the time the ball finally comes to rest at B after several oscillations? Figure 8-68 Problem 87.
SSM A massless rigid rod of length L has a ball of mass m attached to one end (Fig. 8-68). The other end is pivoted in such a way that the ball will move in a vertical circle. First, assume that there is no friction at the pivot. The system is launched downward from the horizontal position A with initial speed v 0 . The ball just barely reaches point D and then stops. (a) Derive an expression for v 0 in terms of L, m , and g. (b) What is the tension in the rod when the ball passes through B ? (c) A little grit is placed on the pivot to increase the friction there. Then the ball just barely reaches C when launched from A with the same speed as before. What is the decrease in the mechanical energy during this motion? (d) What is the decrease in the mechanical energy by the time the ball finally comes to rest at B after several oscillations? Figure 8-68 Problem 87.
SSM A massless rigid rod of length L has a ball of mass m attached to one end (Fig. 8-68). The other end is pivoted in such a way that the ball will move in a vertical circle. First, assume that there is no friction at the pivot. The system is launched downward from the horizontal position A with initial speed v0. The ball just barely reaches point D and then stops. (a) Derive an expression for v0 in terms of L, m, and g. (b) What is the tension in the rod when the ball passes through B? (c) A little grit is placed on the pivot to increase the friction there. Then the ball just barely reaches C when launched from A with the same speed as before. What is the decrease in the mechanical energy during this motion? (d) What is the decrease in the mechanical energy by the time the ball finally comes to rest at B after several oscillations?
two satellites are in circular orbits around the Earth. Satellite A is at an altitude equal to the Earth's radius, while satellite B is at an altitude equal to twice the Earth's radius. What is the ratio of their periods, Tb/Ta
Fresnel lens: You would like to design a 25 mm diameter blazed Fresnel zone plate with a first-order power of
+1.5 diopters. What is the lithography requirement (resolution required) for making this lens that is designed
for 550 nm? Express your answer in units of μm to one decimal point.
Fresnel lens: What would the power of the first diffracted order of this lens be at wavelength of 400 nm?
Express your answer in diopters to one decimal point.
Eye: A person with myopic eyes has a far point of 15 cm. What power contact lenses does she need to correct
her version to a standard far point at infinity? Give your answer in diopter to one decimal point.
Paraxial design of a field flattener. Imagine your optical system has Petzal curvature of the field with radius
p. In Module 1 of Course 1, a homework problem asked you to derive the paraxial focus shift along the axis
when a slab of glass was inserted in a converging cone of rays. Find or re-derive that result, then use it to
calculate the paraxial radius of curvature of a field flattener of refractive index n that will correct the observed
Petzval. Assume that the side of the flattener facing the image plane is plano. What is the required radius of
the plano-convex field flattener? (p written as rho )
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