A block of mass m = 1 kg is sliding at 2 m/s [E] on a frictionless surface. A curved frictionless ramp of unknown mass M is at rest on but not attached to the same frictionless surface, as shown at right. The block slides up the ramp after reaching it. The block rises to a maximum height h = 0.125 m on the ramp. What is the velocity of the block at the instant it is at that maximum vertical height? What is the velocity of the block at the instant the block loses contact with the ramp?
A block is sent up a frictionless ramp along which an x axis extends upward. The figure gives the kinetic energy of the block as a function of position x; the scale of the figure's vertical axis is set by Ks = 34.0 J. If the block's initial speed is 4.00 m/s, what is the normal force on the block? Number Units
A block with mass m = 3.98 kg is placed against a spring on a frictionless incline with angle θ = 38.2∘ (see the figure). (The block is not attached to the spring.) The spring, with spring constant k = 27 N/cm, is compressed 10.9 cm and then released. (a) What is the elastic potential energy of the compressed spring? (b) What is the change in the gravitational potential energy of the block-Earth system as the block moves from the release point to its highest point on the incline? (c) How far along the incline is the highest point from the release point? (a) Number Units (b) Number Units (c) Number Units
A block is sent up a frictionless ramp along which an x axis extends upward. The figure gives the kinetic energy of the block as a function of position x; the scale of the figure's vertical axis is set by Ks = 50.0 J. If the block's initial speed is 6.00 m/s, what is the normal force on the block? Number Units
When a man stands near the edge of an empty drainage ditch of depth 2.80 m, he can barely see the boundary between the opposite wall and bottom of the ditch as in Figure (a) shown below. The distance from his eyes to the ground is h = 1.96 m. (Assume θ = 31.2∘.) (a) What is the horizontal distance d from the man to the edge of the drainage ditch? d = m (b) After the drainage ditch is filled with water as in Figure (b) shown above, what is the maximum distance x the man can stand from the edge and still see the same boundary? x = m
A laser beam is incident at an angle of 32.0∘ to the vertical onto a solution of corn syrup in water. (a) If the beam is refracted to 18.72∘ to the vertical, what is the index of refraction of the syrup solution? (b) Suppose the light is red, with wavelength 632.8 nm in a vacuum. Find its wavelength in the solution. nm (c) Find its frequency in the solution. Hz (d) Find its speed in the solution. m/s
A light ray enters a rectangular block of plastic at an angle of θ1 = 48.0∘ and emerges at an angle of θ2 = 77.5∘ as shown in the figure below. (a) Determine the index of refraction of the plastic. (b) If the light ray enters the plastic at a point L = 50.0 cm from the bottom edge, what time interval is required for the light ray to travel through the plastic? ns
A rope, under a tension of 234 N and fixed at both ends, oscillates in a second-harmonic standing wave pattern. The displacement of the rope is given by y = (0.222 m)sin(πx/6.00)sin(12.0πt) where x = 0 at one end of the rope, x is in meters, and t is in seconds. What are (a) the length of the rope, (b) the speed of the waves on the rope, and (c) the mass of the rope? (d) If the rope oscillates in a third-harmonic standing wave pattern, what will be the period of oscillation? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
The index of refraction for violet light in silica flint glass is 1.66 and that for red light is 1.62. What is the angular dispersion of visible light passing through an equilateral prism of apex angle 60.0∘ if the angle of incidence is 45.0∘? (See figure. The index of refraction for air is 1.00.)
The two mirrors in the figure below meet at a right angle. The beam of light in the vertical plane P strikes mirror 1 at θ1 = 42.5∘ as shown. (a) Determine the distance the reflected light beam travels before striking mirror 2. m (b) In what direction does the light beam travel after being reflected from mirror 2? ∘ above the horizontal
Tarzan, who weighs 870 N, swings from a cliff at the end of a 22.2 m vine that hangs from a high tree limb and initially makes an angle of 25.2∘ with the vertical. Assume that an x-axis points horizontally away from the cliff edge and a y-axis extends upward. Immediately after Tarzan steps off the cliff, the tension in the vine is 787 N. Just then, what are (a) the force from the vine on Tarzan in unit-vector notation, and (b) the net force acting on Tarzan in unit-vector notation? What are (c) the magnitude and (d) the direction (measured counterclockwise from the positive x-axis) of the net force acting on Tarzan? What are (e) the magnitude and (f) the direction of Tarzan's acceleration just then? (a) Number i^ + j^ Units (b) Number i^ + j^ Units (c) Number Units (d) Number Units (e) Number Units (f) Number Units
Suppose a man stands in front of a mirror as shown in the figure below. His eyes are 1.71 m above the floor and the top of his head is 0.13 m higher. Find the height (in m) above the floor of the top and bottom of the smallest mirror in which he can see both the top of his head and his feet. top m bottom m How is the distance d from the top to the bottom of the mirror related to the man's height h? (Use the following as necessary: h.) d =
A square plane mirror of side length a hangs on a wall such that its bottom edge is a height y above the floor. The wall opposite the mirror is a distance w away. Marco, whose eyes are at the exact height of the center of the mirror, stands directly in front of the mirror at the center of its width. Derive an expression for the maximum distance x that Marco can stand from the mirror and still see the reflection of the bottom of the wall behind him. Assume that a < 2y. x = Enter your expression in terms of given values and rational coefficients.