Physics problem for normal force URGENT

Question

Lily, 50kg, Julie 52kg is driving in a car on their way to watch a terrible Manchester United match. The Normal force of the car 10 887.8N at this point. Next they give Robert, 60k, a ride to this terrible match. Calculate the Normal force of the car now that Robert has entered?

Answer 1

Hi Sara! Although I am teaching physics for 40 years, the problem as I say a little bit "politically incorrect" So I will consider 2 cases.

Case 1.

Normal force of the car N₁ = 10 887.8 N is measured, when the girls are already in the car. Because of the addition property of mass (for velocity much less then speed of light) total mass is the sum of all masses. And we see that total mass will be increased by 60 kg, and as a result normal force will be increased by the weight of Rob.

I assume that the car is moving with constant speed and all the time the road is horizontal. Although I haven't seen it in Great Britain.

Then change in N ΔN = m_Rg

Here m_R Rob's mass and g = 9.8 m/s² - acceleration due to gravity.

So new normal force N₂ = N₁ + ΔN or N₂ = N₁ + m_Rg

Plugging in the numeric values we will get: N₂ = 10 887.8 N + 60 kg x 9.8 m/s² = 10 887.8 N + 588 N

Answer: normal force with Rob inside the car N₂ = 11 475,8 N

Case 2.

Normal force of the car alone without girls inside the car is N₁ = 10 887.8 N.

Then total change in normal force ΔN = mg, where m = m_L + m_J + m_R mass of all soccer fans.

And final normal force N₂ = N₁ + ΔN

Putting the values we obtain: m = 50 kg + 52 kg + 60 kg = 162 kg

Now let's find the numeric value of change in normal force. ΔN = 162 kg x 9.8 m/s² = 1 587.6 N

Finally, when all teens are inside the car N₂ = 10 877.8 N + 1 587.6 N = 12 465.4 N

Answer: normal force with Rob inside the car N₂ = 12 465.4 N

My comments:

1. The problem should not be ambiguous.
2. In reality we do not measure the weight of the car with the precision given in the problem.
3. Usually on all exams acceleration of free fall we take 10 m/s² to simplify the calculations.

Good luck!