At a family picnic you are appointed to push your obnoxious cousin Throckmorton in a swing . His weight is w, the length of the chains is R, and you push Throcky until the chains make an angle u0 with the vertical. To do this, you exert a varying horizontal force F S that starts at zero and gradually increases just enough that Throcky and the swing move very slowly and remain very nearly in equilibrium throughout the process. (a) What is the total work done on Throcky by all forces? (b) What is the work done by the tension T in the chains? (c) What is the work you do by exerting force F ? (Ignore the weight of the chains and seat.)

A biker is riding his Yamaha Raptor 700r (atv) on an upward hill in the middle of a desert in dubai. The hill has a slope of theta = 120 degrees. The mass of the atv and biker combined is 260 kg and the static friction coefficient between is .43. Determine the minimum speed of the atv to be able to drive over the hill.

A block of mass 1.96kg is accelerated across a rough surface by a rope passing over a pulley, as shown in the figure below. The tension in the rope is 14.0N, and the pulley is 10.8cm above the top of the block. The coefficient of kinetic friction is 0.350. Calculate the value of x at which the acceleration becomes zero.

A wagon with its passenger sits at the top of the hill. The wagon is giving a slight push and rolls 100. m down an incline (10.0° above the horizontal) to the bottom of the hill. What is the wagon’s speed when it reaches the end of the incline. Assume that the retarding force of friction is negligible. 

A crate of mass m is initially at rest at the highest point of an inclined plane, which has a height of 4.7 m and has an angle of θ = 28° with respect to the horizontal. After it has been released, it is observed to be traveling at v = 0.85 m/s a distance d after the end of the inclined plane as shown. The coefficient of kinetic friction between the crate and the plane is μp = 0.1, and the coefficient of friction on the horizontal surface is μr = 0.2. Find the distance d, in meters.

As shown in the figure below, a box of mass m = 30.0 kg is sliding along a horizontal frictionless surface at a speed v₁ = 4.55 m/s when it encounters a ramp inclined at an angle of 0 = 28.0⁰. frictionless surface The coefficient of kinetic friction between the ramp and the box is μ = 0.0704 and the box slides a distance d up the ramp before coming momentarily to rest. (a) Determine the distance (in m) the box slides up the ramp before coming momentarily to rest. Ο OW₁ = -APE Wg OW, m (b) Determine which of the following statements is most correct about the box traveling up the ramp and coming momentarily to rest. OW.. = AKE Net = W Net ΔΕ = W cons + W noncons ΔΕ = ΔΚΕ + ΔΡΕ Ο O all of these rough surface TTO noncons

A teacher pulls a crate of mass M up the inclined surface the distance d. The surface rises 0 degrees above the horizontal, as shown in the figure. How much does the gravity do on the crate? M=11.9 kg, 0=26.9 degreees, d=5.88 m, g=9.80 m/s^2

A crate of mass m is initially at rest at the highest point of an inclined plane which has a height of 5.28 m and makes an angle of A = 17.2° with respect to the horizontal. After it has been released, it is found to be traveling at v = 0.29 m/s a distance dafter the end of the inclined plane, as shown. The coefficient of kinetic friction between the crate and the plane is tp = 0.1, and the coefficient of friction on the horizontal surface is f4r = 0.2.

A person on an icy expedition is trying to lower a crate of mass m1 = 5.65 kg crate to the bottom of a steep ravine of height h2 21.8 m using a rope over a simple pulley. The person, who m2 frictionless %| weighs m2 = 60.9 kg, is being careful to lower the crate at a constant speed of 1.50 m/s. Unfortunately, when the crate reaches a point h = 12.1 meters above the ground, the person slips and the crate immediately accelerates toward the ground, dragging the hapless person across the ice and toward the edge of the cliff. h If we assume the ice is perfectly slick (that is, no friction between the person and the ice once he slips and falls down), at what speed will the crate hit the ground? Assume also that the rope is long enough to allow the crate to hit the ground before the crewman slides over the side of the cliff. speed: m/s At what speed will the person hit the bottom of the ravine? (Assume no air friction.) speed: m/s

reeee Two blocks and a spring are set up as shown in the picture. The spring is initially unstretched and uncompressed. The system is released from rest. The pulleys are massless. Static friction is not enough to hold it. The coefficient of kinetic friction is = 0.200 for both surfaces. [Use m₁ = 20.0kg, m₂ = 30.0kg, k=80.0, 0 = 30.0°] m a. What is the maximum stretch of the spring? b. How fast are the masses moving after the spring is stretched 0.250m. m, m₂