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NOTE: THE EXPLANATION MUST BE TYPED/ILLUSTRATED DIGITALLY - IT CANNOT BE HAND DRAWN After you pick up a spare, your bowling ball rolls without slipping back toward the ball rack with a linear speed of υi=2.62m/s. To reach the rack, the ball rolls up a ramp that rises through a vertical height of h=0.47m. (a) What is the linear speed of the ball when it reaches the top of the ramp? (b) If the radius of the ball were increased, would the speed found in part (a) increase, decrease, or stay the same? Explain.

An electric motor exerts a constant torque of τ=10N⋅mτ=10N⋅m on a grindstone mounted on its shaft; the moment of inertia of the grindstone is I=2.0kg⋅m2I=2.0kg⋅m2. If the system starts from rest, find the work done by the motor in 8.0 ss and the kinetic energy at the end of this time. What was the average power delivered by the motor?     SOLUTION SET UP AND SOLVE We want to use W=τΔθW=τΔθ to find the total work done and then divide that by the time interval Δt=8.0sΔt=8.0s to find the average power (work per unit time). But first we need to find the total angle ΔθΔθ (in radians) through which the grindstone turns. The angular acceleration αα is constant, so we can use τ=Iατ=Iα to find αα and then apply the formulas for constant angular acceleration. The angular acceleration is α=τI=10N⋅m2.0kg⋅m2=5.0rad/s2α=τI=10N⋅m2.0kg⋅m2=5.0rad/s2 For constant angular acceleration, θ=θ0+ω0t+12αt2=0+0+12(5.0rad/s2)(8s)2=160radθ=θ0+ω0t+12αt2=0+0+12(5.0rad/s2)(8s)2=160rad The total work…

One end of a cord is fixed and a small 0.400-kg object is attached to the other end, where it swings in a section of a vertical circle of radius 1.50 m, as shown in the figure below. When θ = 23.0°, the speed of the object is 5.50 m/s. An object is swinging to the right and upward from the end of a cord attached to a horizontal surface. The cord makes an angle θ with the vertical. An arrow labeled vector v points in the direction of motion. (a) At this instant, find the magnitude of the tension in the string.Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. N(b) At this instant, find the tangential and radial components of acceleration. at = Your response differs from the correct answer by more than 100%. m/s2 downward tangent to the circle ac = Your response differs from the correct answer by more…

A uniform thread of linear mass density λ=2. 0 g/m passes through a fixed ideal pulley. At its ends, the thread is stacked into two heaps that do not interfere motion of the thread. A beetle of mass m=80 g tries to manage itself at a constant height on the thread by adjusting its speed relative to the thread

A ball of mass 2.3 kg, at one end of a string of length L=4.5 m, rotates in a vertical circle just fast enough to prevent the string from going slack at the top of the circle. Assuming mechanical energy is conserved, the speed of the ball (in m/s) at the bottom of the circle is: m a. 10.50 Ob. 8.13 Oc. 9.39 Od. 14.85 Oe. 6.64

There are two wheels. Wheel one has a constant of Ω=2π/3 s^-1 and a radius of 0.3m. Wheel two has a constant a=π/2 s^-2, an initial Ω=-π/10 a d a radius of 0.2m. If these two wheels were to start at x=0, which one would travel 10m first?

A hollow sphere rolls without slipping down a ramp that is 3.5 m long. the ramp is inclined at an angle of 20˚ with the horizontal. Use the conservation of energy to find the speed of the sphere at the bottom of the slope if it starts from rest. ( I= 2/3 m R2 )

Two hangers are attached by a string to a vertically mounted pulley system as shown. One disk is bigger than the other, and the disks are attached to each other such that they rotate together. The axle has negligible friction. The mass of the large disk is 1200 grams and the radius is 11 cm. The mass of the small disk is 400 grams and the radius is 4 cm. The high hanger has a mass of 200 grams and starts 80 cm above the ground. The lower mass starts on the ground and has a mass of 100 grams. The hangers are released from rest. What is the velocity of the 200 gram hanger when it hits the floor?

A thin cylindrical ring starts from rest at a height h1 = 98 m. The ring has a radius R = 34 cm and a mass M = 4 kg. Part (a)  Write an expression for the ring's initial energy at point 1, assuming that the gravitational potential energy at point 3 is zero.  Part (b)  If the ring rolls (without slipping) all the way to point 2, what is the ring's energy at point 2 in terms of h2 and v2?  Part (c)  Given h2 = 32 m, what is the velocity of the ring at point 2 in m/s? Part (d)  What is the ring's rotational velocity in rad/s? Part (e)  After passing point 2 the hill becomes frictionless and the ring's rotational velocity remains constant. What is the linear velocity of the ring at point 3 in m/s?