A block initially at rest slides down a ramp of length L that makes an angle of θ with the horizontal. (a) Derive an equation that predicts the time required for the block to reach the bottom of the ramp in terms of L, θ, g, and μ, the coefficient of friction. (b) This derived equation has no real solutions for angles θ ≤ tan–1 (μ). Show algebraically this is the case and explain the physical significance of this – i.e. what does this mean about an actual block on an actual ramp with actual friction?

If a 3kg box is moving down a ramp with ramp angle 15° and a friction coefficient μk of 0.4, what is the magnitude of the force of friction on the box (in N)?

The maximum ('terminal') velocity, vt, that a falling object achieves depends on its mass m, the acceleration g due to gravity, the density p of the air, the object's frontal area A, and the object's drag coefficient C, which is a dimensionless quantity. The equation for the terminal velocity is: 2mg V = pCA Part (a): A skydiver jumps out of an airplane (regrettably) without his parachute. To slow his descent, he orients himself in a 'spread eagle' position, thereby increasing his area A to 0.70 m?. His drag coefficient Cis 1.0, which is a unitless quantity. Calculate his terminal velocity in m/s if his mass is 85 kg, the air density p is 1.21 kg/m3, and the constant g is 9.80 m/s?. Show your work, and ensure that each numeric value has the appropriate units. Your answer should be rounded to the appropriate number of significant digits. Part (b): Convert the answer from part (a) to miles per hour using the dimensional analysis method we reviewed in class. Show your work, and ensure…

A 1,480-N crate is being pushed across a level floor at a constant speed by a force of 350 N at an angle of 20.0° below the horizontal, as shown in the figure a below. F 20.0° / 20.0° a b (a) What is the coefficient of kinetic friction between the crate and the floor? (Enter your answer to at least three decimal places.) (b) If the 350-N force is instead pulling the block at an angle of 20.0° above the horizontal, as shown in the figure b, what will be the acceleration of the crate? Assume that the coefficient of friction is the same as that found in part (a). m/s²

We often think of friction and air resistance as forces that we want to minimize because they can hinder the motion of an object.  But they are not always undesirable, and in fact, can be an essential element in a machine or process. Identify one or two applications that depend on friction and air resistance.  Explain how friction or air resistance works in those situations and what would happen if there were no friction or air resistance.  Your initial post should be 75-150 words in length and is due on Sunday.

>V=0 d (m A block of mass m is on an inclined ramp. The ramp makes an angle with respect to the horizontal, as shown. The ramp has friction, with coefficient of kinetic friction and static friction μs. This experiment takes place on earth. The block has an initial speed of v up the ramp. It travels a distance d along the ramp before it stops. There are no numbers in this problem! Answer all questions in terms of the given variables (g, m, µk, µs, 8, v, d) only. Do not use any other variables. a) Draw a free body diagram clearly showing all the forces acting on the block while it is moving up the ramp. b) Calculate the work done by the Normal force as the block travels the distance d. Is it positive, negative, or zero? c) Calculate the work done by the Weight force as the block travels the distance d. Is it positive, negative, or zero? d) Calculate the work done by the Friction force as the block travels the distance d. Is it positive, negative, or zero? e) If the block comes to rest,…

Consider the incline shown in the figure with inclination angle θ and height h. The coefficient of kinetic friction between a block of mass m and the incline changes along its surface. From A to B it has a value of μ1, and from B to C its value is μ2. The block (not shown) is given an initial velocity up the incline at point A with a magnitude vA.   A) What is the value of vA for which the block will reach the top of the incline (point C) with zero kinetic energy? Your answer should be written in terms of the quantities given in the statement.   B) Show that for the block to surpass point B, the initial speed at A should satisfy the inequality  vA > √[ (2/3)gh(1+μ1cotθ) ]

A ski that is placed on snow will stick to the snow. However, when the ski is moved along the snow, the rubbing warms and partially melts the snow, reducing the coefficient of friction and promoting sliding. Waxing the ski makes it water repellent and reduces friction with the resulting layer of water. A magazine reports that a new type of plastic ski is especially water repellent and that, on a gentle 230 m slope in the Alps, a skier reduced his top-to-bottom time from 69 s with standard skis to 42 s with the new skis. Old skis acceleration = 0.097 m/s2 New skis acceleration = 0.26 m/s2 Assuming a 3.0° slope, compute the coefficient of kinetic friction for each case. Old skis _______ New skis  _______

A laboratory on the concept of static equilibrium uses an apparatus called a force table. The force table consists of a round, level platform marked in degree increments about its circumference. In the center of the table sits a massless ring, to which three strings are tied. Each string is strung over a m, separate pulley clamped to the edge of the platform, and then m2 tied to a freely-hanging mass, so that each string is under m3 tension and the ring is suspended parallel to the table surface. A mass of m1 = 0.161 kg is located at 0, = 26.5°, and a second mass of m2 = 0.223 kg is located at 02 = 287°. Calculate the mass m3 and the angular position 03 (in degrees) that will balance the system and hold the ring stationary over the center of the platform. 0.239 m3 = kg Incorrect 139 03 Incorrect

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