Jackson finds an old well with a rope, bucket, a shaft that spools the rope, and a large crank wheel that turns the shaft to bring up the bucket of water. The bucket and the water have a total mass of 10.33kg, the shaft has a diameter of 15cm, and the crank wheel has a radius of 0.625m. Ignoring the mass of the rope, use torque to find the tangential force on the crank wheel required to lift the bucket and the water at a constanst speed.

One popular design of a household juice machine is a conical, perforated stainless steel basket 3.30 cm high with a closed bottom of diameter 8.00 cm and open top of diameter 13.40 cm that spins at 23000 revolutions per minute about a vertical axis. Solid pieces of fruit are chopped into granules by cutters at the bottom of the spinning cone. Then the fruit granules rapidly make their way to the sloping surface where the juice is extracted to the outside of the cone through the mesh perforations. The dry pulp spirals upward along the slope to be ejected from the top of the cone. The juice is collected in an enclosure immediately surrounding the sloped surface of the cone. Pulp D Motor Spinning basket Juice spout (a) What centripetal acceleration does a bit of fruit experience when it is spinning with the basket at a point midway between the top and bottom? m/s² ---Direction--- (b) Observe that the weight of the fruit is a negligible force. What is the normal force on 1.50 g of fruit at…

Vlad needs to draw water from a deep well. He is using a bucket that is connected by rope (negligible mass) to a wooden axle at the top of the well. By cranking a handle at the end of the axle, Vlad is able to unwind the rope around the axle and move the bucket downward. The radius of the axle is R = 30 cm. The bucket is traveling downward at speed vi = 25 cm/s when the handle slips out of Vlad’s hand. As the rope unwinds and the bucket falls downward, the axle spins freely with an angular acceleration whose magnitude is α = 4.5 rad/s^2. The bucket falls through a distance of d = 7.0 m before crashing into the water. 1. What is the angular speed ωf of the axle when the bucket first hits the water?  2. As d → 0, what limit does ωf approach and why?

A bicyclist notes that the pedal sprocket has a radius of rp = 8.5 cm while the wheel sprocket has a radius of rw = 6.5 cm. The two sprockets are connected by a chain which rotates without slipping. The bicycle wheel has a radius R = 69 cm. When pedaling the cyclist notes that the pedal rotates at one revolution every t = 1.9 s. When pedaling, the wheel sprocket and the wheel move at the same angular speed.   rp = 8.5 cmrw = 6.5 cmR = 69 cmt = 1.9 s    The pedal sprocket and the wheel sprocket have the same _________  Calculate the angular speed of the pedal sprocket ωp, in radians per second.   Calculate the linear speed of the outer edge of the pedal sprocket vp, in centimeters per second.     Calculate the angular speed of the wheel sprocket ωw, in radians per second.    Calculate the linear speed of the bicycle v, in meters per second, assuming the wheel does not slip across the ground.    If the cyclist wanted to travel at a speed of v2 = 4.5 m/s, how much time, in seconds, should…

Problem 7: Consider the 10.5 kg motorcycle wheel shown in the figure. Assume it to be approximately a ring with an inner radius of 0.28 m and an outer radius of 0.33 m. The motorcycle is on its center stand, so that the wheel can spin freely.

In the figure, what magnitude of force F applied horizontally at the axle of the wheel is necessary to raise the wheel over an obstacle of height h = 0.267 m? The wheel's radius is r = 0.673 m and its mass is m = 1.75 kg. DF

A hanging weight, with a mass of m, = 0.375 kg, is attached by a string to a block with mass m, = 0.865 kg as shown in the figure below. The string goes over a pulley with a mass of M = 0.350 kg. The pulley can be modeled as a hollow cylinder with an inner radius of R, = 0.0200 m, and an outer radius of R, = 0.0300 m; the mass of the spokes is negligible. As the weight falls, the block slides on the table, and the coefficient of kinetic friction between the block and the table is u, = 0.250. At the instant shown, the block is moving with a velocity of v, = 0.820 m/s toward the pulley. Assume that the pulley is free spin without friction, that the string does not stretch and does not slip on the pulley, and that the mass of the string is negligible. (a) Using energy methods, find the speed of the block (in m/s) after it has moved a distance of 0.700 m away from the initial position shown. 1.517 You may have modeled the pulley as a very thin hollow cylinder with a radius of Ra, or as a…

The wheels,axle, and handles of a wheelbarrow weigh W=56N. The load chamber and it’s contents weigh WL=635N.the drawing shows these two forces in two different wheelbarrow designs. To support the wheelbarrow in equilibrium, the man’s hands apply a force to the handles that is directed vertically upward.consider a rotational axis at the point where the tire contacts the ground, directed perpendicular to the plane of the paper.find the magnitude of the man’s force for both designs.

An 80 cm long thin rod whose axis of rotation is in the center has a mass of 0.142 kg. A 2.5 N force is applied at one end perpendicularly, while a second 1.5 N force is applied 10 cm from the opposite end. Both forces are applied in the same direction. (a) Find the angular acceleration. (b) Determine the force needed for the rod to be in equilibrium, if the third force is applied at a 300 angle halfway between the 2.5 N and the axis of rotation. (72.6; -5.5)

A bicyclist notes that the pedal sprocket has a radius of rp = 8.5 cm while the wheel sprocket has a radius of rw = 6.5 cm. The two sprockets are connected by a chain which rotates without slipping. The bicycle wheel has a radius R = 64 cm. When pedaling the cyclist notes that the pedal rotates at one revolution every t = 1.8 s. When pedaling, the wheel sprocket and the wheel move at the same angular speed. a.  Calculate the angular speed of the pedal sprocket ωp, in radians per second.  b. Calculate the linear speed of the outer edge of the pedal sprocket vp, in centimeters per second.  c.  Calculate the angular speed of the wheel sprocket ωw, in radians per second.  d.  Calculate the linear speed of the bicycle v, in meters per second, assuming the wheel does not slip across the ground.