Average force is a conditional size. In cases when force operating on a body changes over time or action of force very little, it is not possible to determine force size in each timepoint. Therefore in these cases accept assumption that in a definite time the body was affected by constant force equal to average and count it - Fcp.
It is required to you
- ability to integrate
Instruction
1. Let the body under the influence of a certain force of F changed the speed from V1 to V2 for a short period Δt. Acceleration of this body will be equal to a=(V2-V1)/Δt where and, V1 and V2 – are vector sizes.
2. Substitute this expression in the seconda formula law of Newton: F=ma=m(V2-V1)/Δt=(mV2-mV1)/Δt, without forgetting that F force – too vector size.
3. Write down the received formula in a bit different look: FΔt=mΔV =Δp. The vector size FΔt equal to the work of force for the period of its influence, call an impulse of force and measure in the newtons increased by a second (H·s). And the work of body weight on its speed p=mV – an impulse of a body or the number of the movement of a body. This vector size is measured in the kilograms increased by meter per second (kg • m/s).
4. Thus the second law of Newton can be formulated differently: the impulse of force operating on a body is equal to change of an impulse of a body: FΔt=Δp.
5. If time of influence of force was very little, for example, during blow, then average force is found so: Fcp =Δp/Δt=m(V2-V1)/Δt. Example: The ball weighing 0.26 kg flew with a speed 10m/page. After blow of the volleyball player, the ball increased speed to 20m/page. Blow time – 0.005 pages. The average force of impact of a hand of the volleyball player on a ball is equal in this case Fcp =0.26 • (20-10)/0.005с = 520H.
6. If force operating on a body is not constant, and changes under the law F(t) over time, then by integration of the F(t) function on t time on an interval from 0 to T find change of an impulse of a body: dp = F(t)dt.
7. And determine value of average force by a formula Fcp =dp/dt. Example: Force changes under linear law F=30t+2 over time. Find the average force of influence for 5 pages. At first we calculate p= body impulse ∫ (30t+2) dt=15t²+2t, and then average force: Fcp = (15t²+2t)/t=15t+2=15·5+2=77H