Question

A 100-g toy car moves along a curved frictionless track. At first, the car runs along a flat horizontal segment with an initial velocity of 2.66 m/s. The car then runs up the frictionless slope, gaining 0.186 m in altitude before leveling out to another horizontal segment at the higher level. What is the final velocity of the car if we neglect air resistance?

Answer 1

Answer:

The final velocity of the car is 1.85 m/s

Explanation:

Hi there!

The initial kinetic energy of the toy car can be calculated as follows:

KE = 1/2 · m · v²

Where:

KE = kinetic energy.

m = mass.

v = velocity.

KE = 1/2 · 0.100 kg · (2.66 m/s)² = 0.354 J

The gain in altitude produces a gain in potential energy. This gain in potential energy is equal to the loss in kinetic energy. So let´s calculate the potential energy of the toy car after gaining an altitude of 0.186 m.

PE = m · g · h

Where:

PE = potential energy.

m = mass.

g = acceleration due to gravity.

h = height.

PE = 0.100 kg · 9.8 m/s² · 0.186 m = 0.182 J

The final kinetic energy will be: 0.354 J - 0.182 J = 0.172.

Using the equation of kinetic energy, we can obtain the velocity of the toy car after running up the slope:

KE = 1/2 · m · v²

0.172 J = 1/2 · 0.100 kg · v²

2 · 0.172 J / 0.100 kg = v²

v = 1.85 m/s

The final velocity of the car is 1.85 m/s