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Aydan Guliyeva

Aydan G.

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A marble is rolling across the floor at a speed of $7.0 \mathrm{m} /$ s when it starts up a plane inclined at $30^{\circ}$ to the horizontal. (a) How far along the plane does the marble travel before coming to a rest? (b) How much time elapses while the marble moves up the plane?

A marble is rolling across the floor at a speed of $7.0 \mathrm{m} /$ s when it starts up a plane inclined at $30^{\circ}$ to the horizontal. (a) How far along the plane does the marble travel before coming to a rest? (b) How much time elapses while the marble moves up the plane?

University Physics Volume 1

Part of riding a bicycle involves leaning at the correct angle when making a turn, as seen below. To be stable, the force exerted by the ground must be on a line going through the center of gravity. The force on the bicycle wheel can be resolved into two perpendicular components-friction parallel to the road (this must supply the centripetal force) and the vertical normal force (which must equal the system's weight). (a) Show that $\theta$ (as defined as shown) is related to the speed $v$ and radius of curvature $r$ of the turn in the same way as for an ideally banked roadway - that is, $\theta=\tan ^{-1}\left(v^{2} / r g\right) .$ (b) Calculate $\theta$ for a 12.0 -m/s turn of radius $30.0 \mathrm{m}$ (as in a race).

Part of riding a bicycle involves leaning at the correct angle when making a turn, as seen below. To be stable, the force exerted by the ground must be on a line going through the center of gravity. The force on the bicycle wheel can be resolved into two perpendicular components-friction parallel to the road (this must supply the centripetal force) and the vertical normal force (which must equal the system's weight). (a) Show that $\theta$ (as defined as shown) is related to the speed $v$ and radius of curvature $r$ of the turn in the same way as for an ideally banked roadway - that is, $\theta=\tan ^{-1}\left(v^{2} / r g\right) .$ (b) Calculate $\theta$ for a 12.0 -m/s turn of radius $30.0 \mathrm{m}$ (as in a race).

University Physics Volume 1

Show that the functions in Exercises have exactly one zero in the given interval. $$g(t)=\frac{1}{1-t}+\sqrt{1+t}-3.1, \quad(-1,1)$$

Show that the functions in Exercises have exactly one zero in the given interval. $$g(t)=\frac{1}{1-t}+\sqrt{1+t}-3.1, \quad(-1,1)$$

University Calculus: Early Transcendentals

Applications of Derivatives

The Mean Value Theorem

The triangle with vertices $(1,1),(1,2),$ and (2,2) about a. the $x$ -axis b. the $y$ -axis c. the line $x=10 / 3$ d. the line $y=1$

Thomas' Calculus: Early Transcendentals in SI Units

Applications of Definite Integrals

Volumes Using Cylindrical Shells

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Crystal Wang verified

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post pandemic era in social psychology

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Richelle Chappell verified

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collisions in multiple dimensions

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Chasen Shaw verified

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An object with mass m1 = 42 kg is located at the origin. Another object with mass m2 = 54 kg is located at l2 = 0.17 m. Consider position la = 0.044 m between the two objects and along the axis connecting them. Refer to the diagram. The gravitational field of m1 is denoted by g1. Enter an expression for the gravitational field g1 at position la in terms of m1, la, and the gravitational constant G.

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When exploring a small planet with a radius of 789 km and a mass of 8.28 x 10^21 kg, a projectile with a mass of 8.12 kg is launched from its surface at escape velocity. Unfortunately, the projectile collides with the spacecraft that is orbiting at an altitude of 1425 km above the surface.With what speed, in meters per second, does the projectile strike the spacecraft?

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Prabhu Ramji verified

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When exploring a small planet with a radius of 524 km and a mass of 7.98 x 1020 kg, a small spacecraft with a mass of 8220 kg is placed in an elliptical orbit around it. When the spacecraft is at a distance of 2150 km from the center of mass of the small planet, it has an orbital speed of 447 m/s.What is the orbital speed, in meters per second, when the spacecraft is at a distance of 12030km from the small planet?

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You are constructing a mobile out of 5 identical toy helicopters, each of mass m = 28.4 g, 4 identical sticks (each length l = 21.4 cm, and negligible mass), and thin string of negligible mass. The distance from the left-hand side of each stick to the attachment point of the sting supporting it are x1 through x4 respectively, as shown in the diagram. The tensions in the supporting strings are T1 through T4 as shown. You want to design the mobile so that it is in static equilibrium.Find the tension in Newtons in the string T1.

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Prabhu Ramji verified

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An ice skater is preparing for a jump with turns and has his arms extended. His moment of inertia is 1.8 kg⋅m2 while his arms are extended, and he is spinning at 0.69 rev/s. Then he simultaneously pulls his arms in and launches himself into the air at 5.3 m/s at an angle of 41∘ with respect to the ice. His moment of inertia in the air is 0.5 kg⋅m2.How long in seconds is the skater in the air? Specify your answer in at least two digits past the decimal point.

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Emily Anderson verified

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A uniform rod of mass M = 2.81 kg and length L 1.14 m can rotate about a hinge = at its left end and is initially at rest. A putty ball of mass m= 65.2 g, moving with speed v = 5.74 m/s, strikes the rod at angle = 52,7degree from the normal at a distance D = 2/3L from the point of rotation, and it sticks to the rod after the collision.What is the angular speed, in radians per second, of the system immediately after the collision?

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Prabhu Ramji verified

Numerade educator

A uniform rod of mass M = 2.81 kg and length L 1.14 m can rotate about a hinge = at its left end and is initially at rest. A putty ball of mass m= 65.2 g, moving with speed v = 5.74 m/s, strikes the rod at angle = 52,7degree from the normal at a distance D = 2/3L from the point of rotation, and it sticks to the rod after the collision.What is the total moment of inertia, If, with respect to the hinge, of the rod-ball-system after the collision?

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Prabhu Ramji verified

Numerade educator

Consider a horizontal spinning disc of radius R=5.7m. A ball of mass m=3.63kg and negligible size is attached, with a clamp, to the outer edge of the disc. The disc starts at rest and experiences a constant angular acceleration, α=3.9rad/s2.Consider the disc at time t=15.9s. Calculate the speed, v, in meters per second, of the attached ball.

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