You will need

- the ability to integrate

Instruction

1

Let the body under the action of a certain force F has changed its velocity from V1 to V2 in a short period of time Δt. The acceleration of the body is equal to a=(V2-V1)/Δt, where a and V1 and V2 are vector quantities.

2

Substitute this expression into the formula for Newton's second law: F=ma=m(V2-V1)/Δt=(mV2-mV1)/Δt, not forgetting that the force F is also a vector quantity.

3

Write down the resulting formula in a slightly different form: FΔt=mΔV =Δp. Vector quantity FΔt, is the product of force at the time of its impact is called the impulse force and measured in Newtons multiplied by the second (N•s). And the product of mass and velocity p=mV – momentum of the body or body movement. This vector quantity measured in kilograms multiplied by meter per second (kg•m/s).

4

Thus Newton's second law can be formulated differently: the impulse of the force acting on a body is equal to change of momentum: FΔt=Δp.

5

If the impact force was very small, for example, during impact, the average

**force**find: Fср=Δp/Δt=m(V2-V1)/Δt.Example: a Ball with a mass of 0.26 kg, flying at a speed of 10m/s. After hitting a player, the ball speed increased to 20 m/s Time of impact is 0.005 s. the Average force the hand of the player on the ball is equal in this case Fср=0,26•(20-10)/0.005=520Н.6

If the force acting on a body is not constant, but changes with time according to the law F(t), by integrating the function F(t) at time t in the interval from 0 to T, find the change of momentum of the body: DP=F(t)dt.

7

And the formula Fср=dp/dt, determine the value of the average power.Example: a Force changing with time according to a linear law F=30t+2. Find the average impact force for 5s. First compute the momentum p=∫(30t+2)dt=15t2+2t , then the average force: Fср=(15t2+2t)/t=15t+2=15•5+2=77Н

Note

Force is a vector quantity. If the result of the calculation value Fср turned out negative, it means that the force vector is directed in the direction opposite to the direction of the coordinate axis.

Useful advice

Don't forget when solving problems to translate everything used in formulas values in SI. Ie, mass in kilograms, speed in meters divided by the second, and force in Newtons.

# Advice 2 : How to determine the force of impact

It often happens that it is necessary to measure the force of impact of the athlete in training for the establishment of any record or report to the coach. There are three methods of determining this value.

You will need

- Target;
- - the accelerometer.

Instruction

1

Use the law of conservation of potential and kinetic energy. We need it to measure the force of impact at the target. First fix the suspension on any target with a mass "m". Produce the impact and measure the value of deviation "h". This can be done using the notches on the beam, on which to fasten the makiwara. The force of the blow will be equal to the value of the formula "mgh", where g is the acceleration of free fall. By this method you can measure the impact energy accurately. Also, this method is very effective for setting for setting all kinds of records. And there, as a rule, the makiwara has an electronic sensor for even more precision.

2

Apply the device with the Doppler effect. In this case, the target is to be secured in the same way as in the previous step. The force of the impact here will be equal to the speed of the target, which propagates the ultrasound. When properly selected approach, the calibration is not required.

3

Measure the energy (force) of impact with precision triaxial or biaxial integral accelerometers. The results are in this case sufficiently accurate. The main advantage of this method is that you can strike in any direction, with the exception of strikes from the top. Although you can simply change the design and measure the strength of such impacts too.

4

Use as a measure of the force of impact of integrated accelerometers with digital output. Their advantage is that they are more sensitive and you will not need additional calibration. If the accelerometer analog output, then you need to use also the value of gravitational acceleration "g" for more accurate data of the force of the blow. The proposed measurement method solves the problem of certainty about the impact energy of the athlete. All this can help in the assessment of physical readiness of the athlete at the moment.

# Advice 3 : How to determine the momentum of the body

The momentum of the body is otherwise called the amount of traffic. It is determined by the product of mass and velocity. It can also be found through the duration of the force on the body. The physical meaning is not the impetus to change.

You will need

- — scales;
- speedometer or the radar;
- — dynamometer;
- calculator.

Instruction

1

Determine the mass

**of a body**with weights in kilograms. Measure its speed. Do this with the speedometer or special radar in meters per second. Calculate the momentum**of the body**p as the product of its mass m to the velocity v (p=m∙v). For example, if the speed**of the body**is 5 m/s and its mass is 2 kg, the momentum is p=2∙5=10 kg∙m/s.2

More important is the ability to find the change in momentum

**of the body**, since momentum is a characteristic of the impact in which this value is changed. To find the change in momentum**of the body**, subtract the final momentum from the initial, considering that the magnitude of this vector. Thus, the change in the momentum of bodies is equal to the vector Δp, which is the difference vector p2 (final momentum) and p1 (the initial impulse).3

If the body does not change direction, in order to find the variation of the pulse, subtract from the finite speed of primary and multiply it to the mass

**of the body**. For example, if the vehicle is moving in a straight line, the rate increased from 20 to 25 m/s, and its mass is 1200 kg, but the change in its momentum will be Δp=1200∙(25-20)=6000 kg∙m/s. If the speed**of the body**decreases, then the change in its momentum will be negative.4

If the body changes direction, looking for the difference between the vectors p2 and p1 using the theorem of the cosines or other relations.

5

Example. A ball of mass 500 g is elastically struck a smooth wall at an angle of 60º to the vertical, and his speed was 3 m/s, find the change in its momentum. Since the collision is elastic, the ball will fly away from a smooth wall is also angled at 60º, with the same velocity, 3 m/s to translate the difference in the amount, multiply the vector by -1 p1. Get that Δp is equal to the sum of vectors p2 and –p1. Applying the triangle rule, calculate Δp=√((0,5∙3)2+ (0,5∙3)2-2∙(0,5∙3)∙(0,5∙3)∙cos(60º))=0,5∙3=1.5 kg∙m/s. it is Noteworthy that the module start and end of a pulse in this case is also 1.5 kg∙m/s.

6

If we know the force acting on the body, which is the reason for changing its speed and duration of its action, then calculate the change of momentum as the product of force F on its duration Δt (Δp=F∙Δt). The power measure dynamometer. For example, if the player hit the ball with a force of 400 N, and the time of impact is equal to 0.2 s, the change in momentum of the ball will be Δp=400∙0,2=8000 kg∙m/s.