Question

A 0.2 kg toy car starts from rest at the top of a hill with a height of 1 m. The inclination of the hill is 30°. At the bottom of the hill, the toy car runs into a horizontal patch of sand and comes to rest. If static friction of the hill is 0.5 and 0.3 and that of the sand is 0.8 and 0.4, find the acceleration of the car when it reaches the sand. (g = 9.8)

Answer 1

To find the acceleration of the car when it reaches the sand, we need to consider the forces acting on it. The main forces to consider are gravity, normal force, and friction. By plugging in the given values and calculating the necessary equations, we can find the acceleration of the car.

Step-by-step explanation:

To find the acceleration of the car when it reaches the sand, we need to consider the forces acting on it. The main forces to consider are gravity, normal force, and friction. At the top of the hill, the car has potential energy which gets converted into kinetic energy as it goes down the hill. When the car reaches the sand, friction comes into play and eventually brings the car to a stop. The acceleration can be found using the equation:

ma = mg sin(angle) - fr

where m is the mass of the car, g is the acceleration due to gravity, angle is the angle of inclination, and fr is the force of friction. The force of friction can be calculated using the formula:

fr = µfN

where µf is the coefficient of friction and N is the normal force. The normal force can be calculated using:

N = m * g * cos(angle)

By plugging in the given values and calculating the above equations, we can find the acceleration of the car when it reaches the sand.