Solving Mechanics Problem: Calculate Coefficient of Friction & Work Done

[Elumalai]

A 40 kg seal at an amusement park slides down a ramp into the pool below. The top of the ramp is 2m higher than the surface of the water and the ramp is inclined at an angle of 45.0° above the horizontal. The seal starts from rest and reaches the water with a speed of 5.1m/s.
(a) What is the coefficient of kinetic friction between the seal and the ramp?

(b) How much work is done by kinetic friction?


Can anybody help me in solving the above problem. I am interested in getting practised in solving problems in physics at graduation level. A list of books where these type of problems are solved in all topics of physics ( Mechanics , Elctricity , Magnetism , Nuclear physics etc ) will be highly helpful to me.

 

[Pheo1986]

ok. so you have the initial velocity, final velocity and hieght. from this you can find the acceleration.

you then know that f=ma and also that f=coefficient of kinetic friction * the reaction force. so now you have acceleration, mass and you can work out the reaction force useing the 45 degree angle, so just rearange to find the coefficient of kinetic friction.

hope this is a gd starting point for you

 

[kerimek]

I am happy to provide a response to this problem and offer some helpful resources for practicing problem-solving in physics at the graduate level.

(a) To calculate the coefficient of kinetic friction, we can use the following formula:

μk = (m*g*sinθ - m*a)/ (m*g*cosθ)

Where μk is the coefficient of kinetic friction, m is the mass of the seal (40 kg), g is the acceleration due to gravity (9.8 m/s^2), θ is the angle of inclination of the ramp (45°), and a is the acceleration of the seal (5.1 m/s^2).

Plugging in these values, we get:

μk = (40*9.8*sin45° - 40*5.1)/ (40*9.8*cos45°) = 0.14

Therefore, the coefficient of kinetic friction between the seal and the ramp is 0.14.

(b) To calculate the work done by kinetic friction, we can use the formula:

W = μk*m*g*d*cosθ

Where W is the work done, μk is the coefficient of kinetic friction (0.14), m is the mass of the seal (40 kg), g is the acceleration due to gravity (9.8 m/s^2), d is the distance traveled by the seal (2m), and θ is the angle of inclination of the ramp (45°).

Plugging in these values, we get:

W = 0.14*40*9.8*2*cos45° = 10.6 J

Therefore, the work done by kinetic friction is 10.6 Joules.

As for resources for practicing problem-solving in physics at the graduate level, here are a few suggestions:

1. "University Physics" by Young and Freedman: This textbook covers all topics of physics, including mechanics, electricity, magnetism, and nuclear physics, and has a variety of challenging problems at the end of each chapter.

2. "Solved Problems in Physics" by Schaum's Outline Series: This book contains over 2,000 solved physics problems, including many at the graduate level.

3. "Problems and Solutions in Introductory Mechanics" by David Morin: This book contains a collection of problems and solutions in mechanics, suitable for students at the graduate level.

4. "Fundamentals of Physics" by Resnick, Halliday