Question

Some sliding rocks approach the base of a hill with a speed of 13 m>s. The hill rises at 42° above the horizontal and has coefficients of kinetic friction and static friction of 0.43 and 0.61, respectively, with these rocks. (a) Find the acceleration of the rocks as they slide up the hill. (b) Once a rock reaches its highest point, will it stay there or slide down the hill? If it stays, show why. If it slides, find its acceleration on the way down.

Answer 1

To find the acceleration of the rocks as they slide up the hill, calculate the net force by subtracting the force of friction from the component of the weight parallel to the slope. To determine if a rock will stay at its highest point or slide down, compare the force pulling the rock down the hill with the force of friction. The acceleration on the way down can be found using the same formula as above, but using the coefficient of static friction instead of kinetic friction.

Step-by-step explanation:

To find the acceleration of the rocks as they slide up the hill, we need to calculate the net force acting on the rocks. The net force can be calculated by subtracting the force of friction from the component of the weight parallel to the slope. The force of friction can be found by multiplying the coefficient of kinetic friction by the normal force. The normal force is equal to the weight of the rock multiplied by the cosine of the angle of the slope. Finally, the acceleration can be found by dividing the net force by the mass of the rock.

To determine if a rock will stay at its highest point or slide down the hill, we need to compare the force pulling the rock down the hill (the component of the weight parallel to the slope) with the force of friction. If the force of friction is greater, the rock will stay at its highest point. If the force pulling the rock down the hill is greater, the rock will slide down. The acceleration on the way down can be found using the same formula as above, but using the coefficient of static friction instead of the coefficient of kinetic friction.

Answer 2

a ) - 8.32 m /s²

b ) 2.06 m /s² down the hill

Step-by-step explanation:

Reaction of the hill surface = mgcos 42

a ) Friction force = μmgcos 42

where μ is coefficient of kinetic friction

Net downward force acting down the hill on rocks

= mgsin32 + μmgcos 42

acceleration

= -gsin32 - μgcos 42

= - 9.8 x .5299 - .43 x 9.8 x cos42

= - 5.19 - 3.13

= - 8.32 m /s²

b ) When it reaches the highest point , it becomes stationary . After that it tries to come down due to its weight.

Force acting downwards

= mgsin 42

5.19 m

Force of friction preventing it to slide down

= mgcos42 x .61 ( static friction will act on it )

= 4.44m

The body will go down with acceleration.

Net acceleration. =

5.19 - 3.13 ( kinetic friction will act on it )

2.06 m /s² down the hill