How Do You Calculate the Mass of a Car Using Force and Acceleration?

[Student3.41]

Homework Statement

To determine the mass of a car, a student (with a friend at the wheel) pushes the car holding a bathroom scale between himself and the car. The scale maintains a constant reading of 433 N while the car accelerates on level ground. At the conclusion of the experiement, his friend reports that the car accelerated from rest to 18.8 km/hr in 15.9 s. What was the mass of the car?

Homework Equations

a= Delta V/Delta t
f=ma
w=mg
g=9.8m/s^2

The Attempt at a Solution

a = 18.8km/hr/15.9s ------> 313m/s/15.9s = 19.7m/s^2 - > Acceleration of car.

F=ma, since the force is constant throughout the problem I assumed acceleration was constant.

W=mg ----> 422N=m(9.8m/s^2)--> m=43.06kg, is the weight.

f=ma ---> f=(43.1kg)(19.7m/s^2) = 847N

m= 847N/9.8m/s^2 = 86.4kg... incorrect.. am i doing too much ?

 

[p21bass]

You're on the right track, but I see two errors, and I'm not sure about one of your steps.

18.8 km/hr does not equal 313 m/s. Hint: how many seconds are there in one hour?

I don't know why you tried calculating the weight - or why you used 422N. I *think* you need to reread the problem, and visualize what they did with the scale, and what the 433N actually represents.

I believe your mass should equal 1318kg, yes?

 

[Student3.41]

You're on the right track, but I see two errors, and I'm not sure about one of your steps.

18.8 km/hr does not equal 313 m/s. Hint: how many seconds are there in one hour?

I don't know why you tried calculating the weight - or why you used 422N. I *think* you need to reread the problem, and visualize what they did with the scale, and what the 433N actually represents.

I believe your mass should equal 1318kg, yes?

Correct.

OK, got to figure out how you did this.

I fixed my stupid mistakes;

v=5.22m/s
a=5.22m/s/15.1s=0.346m/s^2


Now, M=433N/0.346m/s^2--->1251kg

The 433N represents the weight of the car? W(N)=m(kg)a(m/s^2)

 

[p21bass]

"To determine the mass of a car, a student (with a friend at the wheel) pushes the car holding a bathroom scale between himself and the car."

The car isn't on top of the scale, so it's not the weight of the car. If it were the weight of the car, then we'd just divide 433N/9.81(m/s^2). It's the amount of force required to move the car. So you did it correctly this last time, but you somehow put 15.1s into your equation, as opposed to 15.9s.

 

[rwisz]

Your method of using the equations for acceleration and force to determine the mass of the car is correct. However, your final calculation for the mass of the car is incorrect. This may be due to a calculation error or a rounding error. To find the correct mass, use the value for acceleration that you calculated (19.7 m/s^2) and the given force of 433 N. The mass of the car can then be found by dividing the force by the acceleration (m = F/a). This should give a mass of approximately 22 kg. It is important to double check your calculations and be careful with significant figures to ensure accurate results.