How Do You Solve These Impulse and Momentum Problems?

[Riya]

I can't get these at all...

1) A sprinter with a mass of 76 kg accelerates force 0 to 9.4 m/s in 2.8 s. Find the average force acting on the runner.

2) A 0.25 kg soccer ball is rolling at 6.0 m/s towards a player. The player kicks the ball back in the opposite direction and gives it a velocity of -14 m/s. What is the average force during the interaction between the player's foot and the ball if the interaction lasts 2.0 x 10 to -2 s.

3) A force of 1.21 x 10 to 3 N is needed to bring a car moving at +22.0 m/s to a halt in 20.0 s? What is the mass of the car?

4) Small rockets are used to make small adjustments in the speed of satellites. ONe such rocket has thrust of 35 N. If it is fired to change the velocity of 72 000 kg spacecraft by 63 cm/s, how long should it be fired?

5) A 10 000 kg freight car is rolling along a track at 3.00 m/s. Calculate the time needed for a force of 1000 N to stop the car.

6) A car moving at 10 m/s crashes into a barrier and stops in 0.24m.
a) Find the time required to stop the car.
b) If a 20 kg child were to be stopped in the same time as the car, what average force must be exerted?
c) Approximately what is the mass of an object whose weight equals the force from part b? Could you lift such a mass with your arm?
d) What does your answer to part c say about holding a infant on your lap instead of using a separate infant restraint?

 

[Riya]

please help me if you can...

 

[dextercioby]

please help me if you can...

I can help you,but the idea of this homework forum is that people should still do their homeworks all by themselves.We're here just to help,if you get stuck.The policy is that the people in need of assistance should post his/her work and we should check whether it's okay or not.We don't promote laziness.

So please,post your ideas for each problem.

Daniel.

 

[Riya]

I can help you,but the idea of this homework forum is that people should still do their homeworks all by themselves.We're here just to help,if you get stuck.The policy is that the people in need of assistance should post his/her work and we should check whether it's okay or not.We don't promote laziness.

So please,post your ideas for each problem.

Daniel.

Well, thankyou for letting me know...
this is my homework and I've done the previous 16 questions before these already, and mind you if i was lazy i wouldn't be worried about posting the h/w questions up properly... I did work these questions out, but failed to understand them... and you're telling me to repeat that whole thing again... NO thankyou... Maybe a real life tutor is better...

 

[HallsofIvy]

You "failed to understand them"? Each is really a question about basic definitions. You need to know them before you can do anything. Do you know "F= ma"?

 

[DB]

Force, Newtons

$$F=ma$$

Momentum

$$p=mv$$

Impulse, Newton-seconds kg m/s

$$\Delta p=F*\Delta t$$ or $$I=F*t$$

*$$\Delta p$$ is equivilant to Impulse

There is also another equation for Impulse but I'm not exactly sure how to use it.

$$I=\int F*dt$$

These are key formulas to your problems, but i think you know them. I suggest that you identify all the information you are given in each problem seperatly, such as F,m,a,p,t,I and see which equation fits best to solve the unknown.

One thing I would like to know is how to convert 0 to 9.4 m/s in 2.8 s into m/s^2

 

[dextercioby]

I can't get these at all...

1) A sprinter with a mass of 76 kg accelerates force 0 to 9.4 m/s in 2.8 s. Find the average force acting on the runner.

What is the average acceleration with which the spinter is moving in the first 2.8 s?How is related average acceleration aith average force??

2) A 0.25 kg soccer ball is rolling at 6.0 m/s towards a player. The player kicks the ball back in the opposite direction and gives it a velocity of -14 m/s. What is the average force during the interaction between the player's foot and the ball if the interaction lasts 2.0 x 10 to -2 s.

What is the change in momentum (the impulse) the ball gets from the player??How is that connected with the force??

3) A force of 1.21 x 10 to 3 N is needed to bring a car moving at +22.0 m/s to a halt in 20.0 s? What is the mass of the car?

What is the average acceleration acting on the car...??How is that related to force (see problem 1))?

4) Small rockets are used to make small adjustments in the speed of satellites. ONe such rocket has thrust of 35 N. If it is fired to change the velocity of 72 000 kg spacecraft by 63 cm/s, how long should it be fired?

What is the change in momentum the spacecraft suffers due to the interaction with the small rocket??How is that connected with the force/thrust?

5) A 10 000 kg freight car is rolling along a track at 3.00 m/s. Calculate the time needed for a force of 1000 N to stop the car.

What is the average acceleration the force imprimes to the car...??How is that related to time??

6) A car moving at 10 m/s crashes into a barrier and stops in 0.24m.
a) Find the time required to stop the car.
b) If a 20 kg child were to be stopped in the same time as the car, what average force must be exerted?
c) Approximately what is the mass of an object whose weight equals the force from part b? Could you lift such a mass with your arm?
d) What does your answer to part c say about holding a infant on your lap instead of using a separate infant restraint?

a)What is the relation between distance,speed and time?
b) You must find the average acceleration acting on the kid.It's a similar task as before.
c)Find the force at b) and divide through "g" to find the mass.Compare that with the maximum mass u could lift with your arm (i myself couldn't lift more than 20Kg...).
d)I don't know,what's an "infant restraint"??A leash?

Daniel.

 

[DB]

I think this might help with the average acceleration. If we graph the acceleration for example the first problem, we get a linear direct graph.

Since: $$y=ax+b$$ and its is direct we know "b" is 0. Whats left to find is the slope.

Use $$\frac{y_2-y_1}{x_2-x_1}$$

So with 2 consecutive points on the graph being (2.1, 7.35)(2.8, 9.8) we can fill in:

$$\frac{9.8-7.35}{2.8-2.1}=\frac{2.45}{.7}=3.5x$$

Therefore $$y=3.5x$$ being the rate of change of velocity i.e acceleration.

So know we have $$3.5 \frac{m}{s^2}$$ and the mass of sprinter 76000 mg we can easily apply F=ma.

I think this would work. If not let me know.

 

[dextercioby]

Yo,pal,u've been reading other problem.Where did u get those numbers??Your 9.8 is actually 9.4.
By definition the average acceleration on the time interval $[t_{1},t_{2}]$ is
$$a_{avg,t_{1},t_{2}}=:\frac{v(t_{2})-v_{1}(t_{1})}{t_{2}-t_{1}}$$

For this problem chose $t_{1}=0$ and then $t_{2}=2.8s$:the problem gives u that
$$v(t_{2})=9.4ms^{-1};v(t_{1})=0ms^{-1}$$
Plug these 4 values in the definition of average acceleration and find the result
$$a_{avg,0,2.8s}\sim 3.357ms^{-2}$$

Find the average force knowing that the average force is the product between mass and average acceleration.

Daniel.

PS.76Kg=76000g=76000000mg.

 

[DB]

Although I got the numbers mixed up, it still works out. Using $$a_{avg,t_{1},t_{2}}=:\frac{v_2(t_{2})-v_{1}(t_{1})}{t_{2}-t_{1}}$$ with $$v_2$$ being 9.8, The answer for average velocity is also 3.5 m/s^2. Your way is a lot simpler though.

PS.76Kg=76000g=76000000mg.

Yea, my head was stuck on meters so I ended up writing mg.