Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. Each step is of uniform height d. The mass of each object is a multiple of the base mass m: object 1 has mass 3.10m, object 2 has mass 1.46m, and object 3 has mass m. When the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. If the objects are then relocated as shown, what is the new total potential energy of the system? Each answer requires the numerical coefficient to an algebraic expression. Each algebraic expression is given using some combination of the variables m, g, and d, where g is the acceleration due to gravity. Enter only the numerical coefficient. (Example: If the answer is 1.23mgd, just enter 1.23)

A cat's crinkle ball toy of mass 28 g is thrown straight up with an initial speed of 5 m/s. Assume in this problem that air drag is negligible. (a) What is the kinetic energy of the ball (in J) as it leaves the hand? (b) How much work is done (in J) by the gravitational force during the ball's rise to its peak? (c) What is the change in the gravitational potential energy of the ball (in J) during the rise to its peak? (d) If the gravitational potential energy is taken to be zero at the point where it leaves your hand, what is the gravitational potential energy (in J) when it reaches the maximum height? (e) If the gravitational potential energy is taken to be zero at the maximum height the ball reaches, what would the gravitational potential energy (in J) be when it leaves the hand? (f) What is the maximum height the ball reaches (in m)? m

A particle moves along a curved path y(x) = (10 m){1+cos[(0.1 m−1)x]} , from x = 0 to x = 10π m, subject to a tangential force of variable magnitude F(x) = (10 N)sin[(0.1 m−1)x]. How much work does the force do? (Hint: Consult a table of integrals or use a numerical integration program.)

You drop a 2.50 kg book to a friend who stands on the ground at distance D-13.0 m below. If your friend's outstretched hands are at distance d-1.60 m above the ground (see the figure), (a) how much work W, does the gravitational force do on the book as it drops to her hands? (b) What is the change AU in the gravitational potential energy of the book-Earth system during the drop? If the gravitational potential energy U of that system is taken to be zero at ground level, what is U (c) when the book is released and (d) when it reaches her hands? Now take U to be 100 J at ground level and again find (e) W. (f) AU, (g) U at the release point, and (h) U at her hands. 10000 El

A cat's crinkle ball toy of mass 15 g is thrown straight up with an initial speed of 3 m/s. Assume in this problem that air drag is negligible. (a) What is the kinetic energy of the ball as it leaves the hand? (b) How much work is done by the gravitational force during the ball's rise to its peak? (c) What is the change in the gravitational potential energy of the ball during the rise to its peak?

You go for a walk one afternoon down a level street to a park where there is a hill.  If the hill is 62 meters above street level and 4.6 km  from home , how much work in the physics sense do you do in order to get to the top of the hill?  Assume your mass is 65 kg and the acceleration of gravity is 9.8 m/s. Give your answer in joules (J).

A tennis ball of mass m = 0.091kg is thrown straight up with an initial speed v_{0} = 14m / s Let the gravitational potential energy be zero the initial height of the tennis ball a.what is the maximum height , h in meters the ball reaches B. What is the work done by gravity W_{g} Joules, during the ball's flight to its maximum height?

A dock worker pushes am = 2.20 kg bin a distance d = 2.40 m along the floor by a constant force of magnitude F = 16.0 N directed at an angle 0 = 20.0° below the horizontal as shown in the figure. Assume the floor is frictionless. (Enter your answers in joules.) (a) Determine the work done on the bin by the applied force (the force on the bin exerted by the dock worker). (b) Determine the work done on the bin by the normal force exerted by the floor. (c) Determine the work done on the bin by the gravitational force. (d) Determine the work dong by the net force on the bin.

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Problem Thirteen. A potential energy function is given by U(r)=U2 where o = 2.00 m r r and U, = 1.00 J. Find the magnitude of the force at r= 1.00 m. Give an answer in kN. 25.) (A) 280 (В) 106 (С) 420 (D) 470 (E) 530