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 2.0 meters down the ramp, then another 3.0 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.

Note: The user has mastered the concept of the conservation of energy and is proficient in solving problems where energy is conserved but is new to solving energy problems involving work done by non-conservative forces. Explain how work is related to the total mechanical energy of a system, then use this information to set up and solve the problem above.

Answer 1

Step 1

Given :

mass of toy car = 1 kg

g = 10 m/s²

Force = 2 N

rolling distance = 2 m

speed = 4.24 m/s

Displacement = 3 m + 2 m

                      = 5 m

Step 2

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

By conservation of energy, we can say that work done by air resistance is equal to the sum of kinetic energy and potential energy: ∆P.E + ∆K.E = work done">∆P.E + ∆K.E = work done∆P.E + ∆K.E = work done

                                     (0 - mgh ) + ( 1/2 mv² - 0) = f x s ,and

Work Done = Force x Displacement

substituting the values :

therefore , [1/2 (1) x (4.24)² - 0 ] + [ 0 - (1) (10) h ] = 10

8.98 = 10+10 h

h = 0.898 + 1

h = 1.898 m

 

Step 3

Work done is equal to the change in mechanical energy.

h = 1.898 m