Physics problem to fine average force

[rachels5]

A set of crash tests consists of running a test car moving at a speed of 11 m/s (24.2 m/h) into a solid wall. Strapped securely in an advanced seat belt system, a 57 kg (125.4 lbs) dummy is found to move a distance of 0.81 m from the moment the car touches the wall to the time the car is stopped. Calculate the size of the average force which acts on the dummy during that time.

I do not get this question, i have been working on it for days but i am extremely frustrated

I used the equation
v^2 + u^2 = 2as

where v = final velocity, u = initial velocity, a = acceleration, s = displacement.
so i said
0^2 + 11^2=2(a)(0.81)
It gave me the wrong answer.
but i think that i have to use mass, and my teacher has not shown me a formula in which mass is included

 

[Doc Al]

Show what you've done and where you are stuck.

Hints: You can solve this using energy methods (consider the work done by the wall) or kinematics (find the average acceleration).

 

[rachels5]

can you answer it now .

 

[Doc Al]

I used the equation
v^2 + u^2 = 2as

That should be v^2 = u^2 + 2as.

where v = final velocity, u = initial velocity, a = acceleration, s = displacement.
so i said
0^2 + 11^2=2(a)(0.81)
It gave me the wrong answer.

That will give you the acceleration. Then use Newton's 2nd law to find the net force. (Yes, you'll need the mass.)

 

[asteriatic]

Don't worry, it's completely normal to feel frustrated when tackling a difficult physics problem. Let's break it down step by step and see if we can figure out the correct answer.

First, let's identify the given information:
- Test car speed: 11 m/s
- Dummy mass: 57 kg
- Dummy displacement: 0.81 m

Next, we need to determine what equation to use. Since we are looking for the average force, we can use the equation F=ma, where F is force, m is mass, and a is acceleration. We can also use the equation v^2=u^2+2as, which you have already attempted to use. Both equations are valid, but it's important to use the correct values for each variable.

Using the first equation, F=ma, we need to find the acceleration of the dummy. To do this, we can use the equation a=v/t, where v is the final velocity and t is the time taken for the car to stop. From the given information, we know that the final velocity is 0 m/s (since the car stops) and the initial velocity is 11 m/s. We can also calculate the time taken for the car to stop using the equation t=s/v, where s is the displacement and v is the initial velocity. Plugging in the values, we get t=0.81/11=0.0736 seconds.

Now, we can calculate the acceleration using the equation a=v/t=11/0.0736=149.46 m/s^2.

Finally, we can plug in the values for mass (57 kg) and acceleration (149.46 m/s^2) into the equation F=ma to get the average force: F=(57)(149.46)=8546.22 N.

Using the second equation, v^2=u^2+2as, we can calculate the acceleration directly. Plugging in the values, we get a=(0)^2-(11)^2/2(0.81)=-72.839 m/s^2. This is a negative value because the car is decelerating. We can then use this value for acceleration and the given mass (57 kg) to calculate the average force: F=(57)(-72.839)=-4150.623 N.

It's important to note that both equations give slightly different answers, but this is due to