how do find ave net force?

Question

a 45kg swimmer starting from rest can develop a maximum speed of 12 m/s over a distance of 20 m. how much net force must be applied to do this?

Answer 1

If you know about the work-(kinetic) energy theorem, you can also use this method:

 

W_net = ΔKE = KE_f - KE_o = (1/2)mv_f² - (1/2)mv_o² = (1/2)m(v_f² - v_o²)

 

with

 

W_net = net work (done by the net force)

KE = kinetic energy = (1/2)mv²

m = 45 kg

v_o = 0 m/s (starts at rest)

v_f = 12 m/s (final speed)

 

So you can solve for the net work done by the net force.  Then, making the reasonable assumption that the net force is along the line of motion (displacement), we can use the other definition for net work:

 

W_net = F_netd

 

where

 

d = distance (= 20 m in this case)

F_net = net force

 

Now, since you calculated W_net above, and you know d, you can use this expression to solve for F_net.

 

However, if you have not yet dealt with work and energy, Arturo's method is the one to use.

Answer 2

Use a kinematic relation to get the acceleration, and then use Newton's 2nd law to get the force.

 

Kinematic relation:

 

v_f² - v_i² = 2ax

 

v_f = final speed = 12 m/s

v_i = initial speed = 0 m/s (started from rest)

a = acceleration = ?

x = distance over which the force was applied = 20 m

 

a = v_f² / (2x) = 12²/[2(20)] m/s² = 3.6 m/s²

 

Newton's 2nd law:

 

F = ma = (45 kg)(3.6 m/s²) = 162 N