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# Conservation of Energy

1. An object of mass 0.23 kg is initially at the origin and is acted on by the sole force F=(0.50 N)i. After a certain amount of time, the object is at a position r=(0.80 m)i. What is the changed in the object's kinetic energy?

2. 74 gram ball is tossed straight up in the air, rises to a maximum point, then falls back until it is .6 m below the position of the hand that tossed it up. A second ball is simply dropped from the same hand position and also lands 0.60 m below that position. What is the net work done by gravity in the two cases?

3. The net force acting on a particle depends on the position of the particle on the x-axis according to the relation F=Fo +Cx, w here Fo=5N and C=-2N/m. The particle is initially at rest at the point x=0 m when the force begins to act. (a) Calculate the work done by the force when the particle reaches x values of 1, 2, 3, and 4 m. (b) Determine any positions (other than at x=0 m) where the work done is zero. (c) Is the force conservative?

4. The maximum power of a particular horse is 1 hp. With what speed can this horse pull a sled on level ground if the weight of the sled with its load is 5000 N and the coefficient of kinetic friction is Mk = 0.03? What is the maximum speed on a 5-degree upward incline?

#### Solution Preview

Answer is in the attached file as well. Thank You.
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1. An object of mass 0.23 kg is initially at the origin and is acted on by the sole force F=(0.50 N)i. After a certain amount of time, the object is at a position r = (0.80 m)i. What is the change in the object's kinetic energy?

Change in energy = change in kinetic energy (since the object moves in the same level it's potential energy remains same)
Change in energy = change in kinetic energy = force * distance = 0.50 * 0.80 = 0.4 J

2. 74 gram ball is tossed straight up in the air, rises to a maximum point, then falls back until it is .6 m below the position of the hand that tossed it up. A second ball is simply dropped from the same hand position and also lands 0.60 m below that position. ...

#### Solution Summary

Four questions on Mechanics have been answered.

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