Question

A toy car with a mass of 1 kg starts from rest at the top of a ramp at point A. The toy car is released from rest, rolls 2 meters down the ramp, then another 3 meters across the floor to point B where its speed is measured to be 4.24 m/s. The air exerts a resistance force of 2.0 N on the car as it moves from A to B. Find the initial height of the car at point A. Assume g = 10 m/s^2.​

Answer 1

Answer:

$h$=1.898m

Explanation:

ΔKE+ΔPE= work done by air resistance

Work done= force(displacement)=-2(3+2)

∴ {${\frac{1}{2}(1)(4.24)^{2} -0}$}+{$0-(1)(10)(h)$} = -2(3+2)

  8.98=-10+10($h$)

  $h$=0.898+1=1.898m

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Answer 2

The initial height is 1.898 m.

Explanation:

Given that,

Mass of toy car = 1 kg

Rolling dustance = 2 m

Distance = 3 m

Speed = 4.24 m/s

Force = 2.0 N

We need to calculate the initial height of the car at point A.

Using conservation of energy

$\Delta P.E+\Delta K.E= \text{work done}$

$(0-mgh)+(\dfrac{1}{2}mv^2-0)=f\times s$

Put the value into the formula

$-1\times10\times h+\dfrac{1}{2}\times1\times(4.24)^2=2.0\times(2+3)$

$-10h=-8.98+10$

$h=\dfrac{8.98+10}{10}$

$h=1.898\ m$

Hence, The initial height is 1.898 m.

Learn more :

Topic : conservation energy

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