# 4.3 Newton’s second law of motion: concept of a system  (Page 5/14)

 Page 5 / 14

## What rocket thrust accelerates this sled?

Prior to manned space flights, rocket sleds were used to test aircraft, missile equipment, and physiological effects on human subjects at high speeds. They consisted of a platform that was mounted on one or two rails and propelled by several rockets. Calculate the magnitude of force exerted by each rocket, called its thrust $\mathbf{\text{T}}$ , for the four-rocket propulsion system shown in [link] . The sled’s initial acceleration is $\text{49}\phantom{\rule{0.25em}{0ex}}{\text{m/s}}^{2},$ the mass of the system is 2100 kg, and the force of friction opposing the motion is known to be 650 N.

Strategy

Although there are forces acting vertically and horizontally, we assume the vertical forces cancel since there is no vertical acceleration. This leaves us with only horizontal forces and a simpler one-dimensional problem. Directions are indicated with plus or minus signs, with right taken as the positive direction. See the free-body diagram in the figure.

Solution

Since acceleration, mass, and the force of friction are given, we start with Newton’s second law and look for ways to find the thrust of the engines. Since we have defined the direction of the force and acceleration as acting “to the right,” we need to consider only the magnitudes of these quantities in the calculations. Hence we begin with

${F}_{\text{net}}=\text{ma},$

where ${F}_{\text{net}}$ is the net force along the horizontal direction. We can see from [link] that the engine thrusts add, while friction opposes the thrust. In equation form, the net external force is

${F}_{\text{net}}=4T-f.$

Substituting this into Newton’s second law gives

${F}_{\text{net}}=\text{ma}=4T-f.$

Using a little algebra, we solve for the total thrust 4 T :

$4T=\text{ma}+f.$

Substituting known values yields

$4T=\text{ma}+f=\left(\text{2100 kg}\right)\left({\text{49 m/s}}^{2}\right)+\text{650 N}.$

So the total thrust is

$4T=1.0×{\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}\text{N},$

and the individual thrusts are

$T=\frac{1.0×{\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}\text{N}}{4}=2.6×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}\text{N}.$

Discussion

The numbers are quite large, so the result might surprise you. Experiments such as this were performed in the early 1960s to test the limits of human endurance and the setup designed to protect human subjects in jet fighter emergency ejections. Speeds of 1000 km/h were obtained, with accelerations of 45 $g$ 's. (Recall that $g$ , the acceleration due to gravity, is $9\text{.}{\text{80 m/s}}^{2}$ . When we say that an acceleration is 45 $g$ 's, it is $\text{45}×9\text{.}{\text{80 m/s}}^{2}$ , which is approximately ${\text{440 m/s}}^{2}$ .) While living subjects are not used any more, land speeds of 10,000 km/h have been obtained with rocket sleds. In this example, as in the preceding one, the system of interest is obvious. We will see in later examples that choosing the system of interest is crucial—and the choice is not always obvious.

Wheatstone bridge problems
what is motion
When a body changes its position with respect to its surroundings then it is said to be in motion
Jon
it is a change in position, direction, shape and arrangement of a body or an object which is initially at rest
Abolarin
Pls guys am having problem on these topics: latent heat of fusion, specific heat capacity and the sub topics under them.Pls who can help?
Thanks George,I appreciate.
hamidat
this will lead you rightly of the formula to use
Abolarin
Most especially it is the calculatory aspects that is giving me issue, but with these new strength that you guys have given me,I will put in my best to understand it again.
hamidat
you can bring up a question and let's see what we can do to it
Abolarin
I also have a problem with the calculation sincerely
Sulaimon
the distance between two suasive crests of water wave traveling of 3.6ms1 is 0.45m calculate the frequency of the wave
v=f×lemda where the velocity is given and lends also given so simply u can calculate the frequency
Abdul
You are right my brother, make frequency the subject of formula and equate the values of velocity and lamda into the equation, that all.
hamidat
lExplain what happens to the energy carried by light that it is dimmed by passing it through two crossed polarizing filters.
When light is reflected at Brewster's angle from a smooth surface, it is 100% polarizedparallel to the surface. Part of the light will be refracted into the surface.
Ekram
What is specific heat capacity?
Specific heat capacity is the amount of heat required to raise the temperature of one (Kg) of a substance through one Kelvin
Paluutar
formula for measuring Joules
I don't understand, do you mean the S.I unit of work and energy?
hamidat
what are the effects of electric current
What limits the Magnification of an optical instrument?
Lithography is 2 micron
Venkateshwarlu
what is expression for energy possessed by water ripple
what is hydrolic press
An hydraulic press is a type of machine that is operated by different pressure of water on pistons.
hamidat
what is dimensional unite of mah
i want jamb related question on this asap🙏
What is Boyles law
it can simple defined as constant temperature
Boyles law states that the volume of a fixed amount of a gas is inversely proportional to the pressure acting on in provided that the temperature is constant.that is V=k(1/p) or V=k/p
what is motion
getting notifications for a dictionary word, smh
Anderson