A book whose mass is 3 kg is projected up a long 40 degree incline with an initial speed of 25 m/s The coefficient of kinetic friction between the book and the Mane is 0.20.
a. Find the magnitude of the friction force acting on the book as it moves up the plane.
b. For how much time does the book move up the plane?
c. How far does the book move up the plane?
d. How much time does it take the book to slide from its position in part (c) back to its starting point?
e. With what speed does it arrive at this point?
A car weighing 9800 N moves around a circular track of 70 m in 60 s.
a. What is the speed or the car?
b. What is the centripetal acceleration?
c. What is the centripetal force?
d. What is the coefficient of friction between the tires and the road?
What is the kinetic energy of the mass at the bottom.
That kenergy must equal mgh (Potential energy gained) + frictional losses (mu*mg*SinTheta*distance) where distance = h/sinTHeta.
I will be happy to critique your thinking on the rest.
Thanks, I will have an Exam tomorrow, so Please, tell me how to do it!!!
Sure! I'll guide you through the steps to solve each problem. Let's start with the first set of questions about the book on the incline:
a. To find the magnitude of the friction force acting on the book as it moves up the plane, we need to consider the forces involved. The book experiences its weight force (mg), the normal force (N) exerted by the incline, and the friction force (f). The weight force can be split into two components: one parallel to the incline (mg*sinθ) and one perpendicular to the incline (mg*cosθ). The friction force acts against the motion and is equal to the coefficient of kinetic friction (μ) multiplied by the normal force (f = μN).
b. To determine the time it takes for the book to move up the plane, we need to use the equations of motion. The initial vertical velocity (v₀) is given as 25 m/s, and since the incline is frictional, the acceleration will be negative due to gravity (-g*sinθ). We can use the kinematic equation: 0 = v₀ + at, where we solve for time (t).
c. To calculate the distance the book moves up the plane, we can use the equation of motion: Δy = v₀t + (1/2)at², where Δy is the displacement along the incline.
d. To find the time it takes for the book to slide from its position in part (c) back to its starting point, we can again use the kinematic equation: 0 = v + at.
e. Finally, to determine the speed with which the book arrives back at the starting point, we need to calculate the final velocity (v). We can use the equation: v = v₀ + at.
Now, let's move on to the second set of questions about the car on the circular track:
a. To find the speed of the car, we can use the formula: speed = distance / time.
b. The centripetal acceleration of the car can be calculated using the formula: a = v² / r, where v is the velocity and r is the radius of the circular track.
c. The centripetal force acting on the car is given by the equation: F = m * a, where m is the mass of the car.
d. Finally, to determine the coefficient of friction between the tires and the road, we need to consider the centripetal force and compare it to the maximum frictional force that can be exerted between the tires and the road. The maximum frictional force can be found using the formula: frictional force = coefficient of friction * normal force.
For the last question regarding kinetic energy at the bottom, you correctly stated the equation: kenergy = mgh + frictional losses. Just make sure you substitute the values correctly into the equation.
I hope this provides you with a starting point to solve the problems! Remember to double-check your calculations and units. Good luck with your exam!