Work
Is work performed here? Yes as long as there is displacement!
Work is done on an object when an applied force moves it through a distance. It is a scalar. Work is defined as Work = Force x Displacement or
W = Fd
sometimes s is used to indicate displacement (W = Fs). The units used is Joules (J) or Newton*meters or kg *m/s2. One Joule is the work done by a force of 1 Newton when it displaces an object one meter in the direction of the force. Keep in mind that you must use the component of the force that acts in the direction of the displacement.
When force is applied at an angle,
W = FscosØ
If F and s are in the same direction, cosØ = 1 and if F and s are in opposite directions, then cosØ = -1.
Suppose force decreases over a period of time at a constant rate. To calculate this, you would use the formula
W = 1/2d(F1 + F2)
Power is the rate of doing work
P = W/t
where t = time during which work is accomplished. Another formula for power is
P = F
where v is the average velocity. The unit for power is the Watt (W). 1W = 1 J/s. 1 hp = 746 J/s.
Machines
Efficiency =(MA/IMA) x 100% =(Wo/Wi) x 100% =(Frdr/Fede) x 100%
where MA = mechanical advantage; IMA = ideal mechanical advantage; Wo = work output; Wi = work input
MA = Fr/Fe
IMA = de/dr
Review Questions:
1. Amanda who weighs 700 N rides an elevator up two levels. (a) The elevator rises 15 meters. (b) On the way down, she is joined by Crystal and Brandie. The combined weight is 2000 N. The elevator descends 15 meters. Assuming that the elevator moves at constant velocity, how much work is done on the passengers in each case?
a. 10,500 J
b. -30,000 J Remember to use a minus sign when the force acts in the opposite direction as the displacement!
2. Nely lifts her book sack which weighs 185 N. It is lifted 0.800 m. How much work does she do on the book sack?
148 J
3. Dan and Greg together exert a force of 825 N in pushing a car 35 m. How much work do they do on the car?
2.9 x 10*4 J
4. Chris drops a 0.180 kg boot which falls 2.5 m. How much work does the force of gravity do on the boot?
4.4 J
5. Aklilu lifts a box 1.2 m with a forklift doing 7.0 kJ of work on it. What is the mass of the box?
6.0 x 10*2 kg
6. Cassie gets a present that weighs 575 N and is lifted a distance of 20.0 m straight up by a cable attached to a motor. The job is done in 10.0 seconds. What power is developed by the motor in watts and kilowatts?
1.15 x 10*3 W or 1.15 kW
7. William goes rock climbing wearing a 7.7 kg knapsack while scaling a cliff. After 30 minutes, he is 8.2 m above the starting point. (a) How much work does William do on the knapsack? (b) If William weighs 645 N, how much work does he do lifting himself and the knapsack? (c) What is the average power developed by William?
a. 6.0 x 10*2 J
b. 5.9 x 10*3 J
c. 3 W
8. If an electric motor develops 65 kW of power as it lifts a loaded elevator 17.5 m in 35 s, how much force does the motor exert?
1.3 x 10*5 N
9. David uses a sledgehammer to drive a wedge into a log to split it. When the wedge is driven 0.20 m into the log, the log is separated a distance of 5.0 cm. A force of 1.9 x 104 N is needed to split the log and the sledgehammer exerts a force of 9.8 x 103 N. (a) What is the IMA of the wedge? (b) Find the MA of the wedge. (c) What is the efficiency of the wedge as a machine?
a. IMA = 4.0
b. MA = 1.9
c. efficiency = 48%
10. Amanda exerts a force of 225 N on a lever to raise a 1.25 x 103 N rock a distance of 13 cm. If the efficiency of the lever is 88.7%, how far did she move her end of the lever?
0.81 m
