Homework Help for Work, Power, & Energy

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1. When work is done against gravity, the force is equal to the weight (not the mass) of the object being lifted, the distance is the vertical height of the lift.
2. (a) same as # 1 (b) no friction here so work is only being done against gravity (c) with any ideal (frictionless) machine, work input = work output--your input is the work you actually did using the machine (force x distance), the output is what you would have had to do without the machine; set equal and solve for force.
3. Here the work is being done against friction. Find the frictional force--that is equal to the force doing the work.
4. In this problem, the force is not aligned with the displacement. Find the component of the force in the same direction as the displacement to calculate the work.
5. The pulley system is not frictionless so there are losses. Efficiency = work out/work in. The work output is the work calculated in #1.
6. Average power equals work divided by elapsed time.
7. Rotary work problem: calculate torque, multiply times angular displacement. Watch the units!
8. Typical power calculation--see # 6
9. Lever problem: work output equals work input.
10. Use efficiency to find work input, then solve for distance.
14. Draw a diagram. Find the weight and its components parallel to the plane and perpendicular to it. Calculate the friction force using the normal component and the coefficient. You are doing work here against gravity and friction both. The work against gravity can be found using the parallel component of weight and the distance. For the work against friction, use the friction force.

Page 130
1. E_P= mgh
2. Convert speed to m/s; E_K=mv²/2
3. E_P=kd²/2; watch the units
4. Conservation of energy problem.
6. Part of work is done against friction, the rest is increasing speed. The work that isn't accounted for in the energy of the box was lost due to friction. Calculate work done (Fd) and kinetic energy.
10. (a) Ball has both rotary and linear kinetic energy. To find the rotary energy, use the rotational inertia for a solid sphere found on page 105. Express angular velocity in terms of linear velocity and radius. When rotational inertia and angular velocity spuared are multiplied together, the radius cancels out and is therefore not necessary for the problem. (b) Ball will roll up the incline until all kinetic energy is converted to potential energy. Set these quantities equal and solve for h. Remember, this is the vertical height, not the distance up the plane. Use trig to find the distance.
11. Conservation of energy problem--find energy of arrow and solve for speed. Watch the units!
12.(a) Initial potential energy will equal kinetic energy at the bottom--solve for speed. (b) Kinetic energy of car is now the difference between the potential energy at the beginning and the potential energy at the top of the second hill. (c) That's the easiest way