Sliding down incline with friction

In summary, a 44.9-kg seal at an amusement park slides down a ramp into a pool with a ramp angle of 33.9° and a distance of 1.80 m. The seal reaches the water with a speed of 4.51 m/s. The work done by kinetic friction cannot be determined without knowing the coefficient of kinetic friction between the seal and the ramp. Setting up a freebody diagram and listing known variables can help find a formula to solve for the coefficient. Without friction, the starting potential energy would equal the final kinetic energy. However, since there is work done by friction, the total KE+PE throughout the slide will decrease.
  • #1
alan_g
1
0
A 44.9-kg seal at an amusement park slides from rest down a ramp into the pool below. The top of the ramp is 1.80 m higher than the surface of the water and the ramp is inclined at an angle of 33.9° above the horizontal. If the seal reaches the water with a speed of 4.51 m/s, what is the work done by kinetic friction?

What is the coefficient of kinetic friction between the seal and the ramp?





i set up a freebody diagram and drew all the forces that would be acting on the seal and listed the known variables, but i can't seem to find a way to connect them all together or find a formula to use to find the work done by kinetic friction or the coefficient of kinetic friction
 
Physics news on Phys.org
  • #2
alan_g said:
A 44.9-kg seal at an amusement park slides from rest down a ramp into the pool below. The top of the ramp is 1.80 m higher than the surface of the water and the ramp is inclined at an angle of 33.9° above the horizontal. If the seal reaches the water with a speed of 4.51 m/s, what is the work done by kinetic friction?

What is the coefficient of kinetic friction between the seal and the ramp?





i set up a freebody diagram and drew all the forces that would be acting on the seal and listed the known variables, but i can't seem to find a way to connect them all together or find a formula to use to find the work done by kinetic friction or the coefficient of kinetic friction

If there were no friction, what could you say about the starting potential energy PE and the final kinetic energy KE? Since there is work done by friction while the slimy seal slides, how will that affect the KE+PE total throughout the slide?
 
  • #3
. Can you please provide some guidance?

Based on the given information, we can use the work-energy theorem to calculate the work done by kinetic friction. The work-energy theorem states that the work done by all forces acting on an object is equal to the change in the object's kinetic energy. In this case, the only force acting on the seal that would do work is the force of kinetic friction.

The formula for the work done by a force is W = Fd, where W is work, F is the force, and d is the distance over which the force is applied. In this case, the distance over which friction is acting is the length of the ramp, which can be calculated using the given angle and height difference.

Next, we need to calculate the force of kinetic friction. We can use the formula Ff = μkN, where Ff is the force of kinetic friction, μk is the coefficient of kinetic friction, and N is the normal force. The normal force in this case is equal to the weight of the seal, which can be calculated as mg, where m is the mass of the seal and g is the acceleration due to gravity.

Now, we can substitute these values into the work formula to get:

W = Ff * d = μk * mg * d

To find the coefficient of kinetic friction, we need to rearrange the formula to isolate μk:

μk = W / (mgd)

Plugging in the values for W, m, g, and d, we get:

μk = (44.9 kg * 9.8 m/s^2 * 1.80 m * sin(33.9°)) / (44.9 kg * 9.8 m/s^2 * cos(33.9°) * 1.80 m)

Solving this equation, we get a coefficient of kinetic friction of approximately 0.317.

Finally, to find the work done by kinetic friction, we can plug in the values for Ff and d into the work formula:

W = Ff * d = (0.317) * (44.9 kg * 9.8 m/s^2 * 1.80 m * sin(33.9°))

Solving this equation, we get a work done by kinetic friction of approximately 113.9 Joules.

In summary, the work done by kinetic friction is 113.9 Joules and the
 

What is the concept of sliding down an incline with friction?

The concept of sliding down an incline with friction involves an object moving down a sloped surface while experiencing resistance from friction. This occurs when the force of gravity pulling the object down the incline is opposed by the frictional force between the object and the surface it is sliding on.

How does the angle of the incline affect the object's descent?

The angle of the incline plays a significant role in determining the object's descent. As the angle increases, the force of gravity pulling the object downwards also increases, resulting in a faster descent. However, the frictional force also increases with a steeper incline, which can slow down the object's descent.

What factors can influence the amount of friction on the incline?

The amount of friction on the incline can be influenced by various factors such as the material of the object and the surface it is sliding on, the weight of the object, and the smoothness of the surface. These factors can affect the coefficient of friction, which is a measure of the resistance between two surfaces in contact.

How can one calculate the acceleration of an object sliding down an incline with friction?

To calculate the acceleration of an object sliding down an incline with friction, one can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. By considering the forces of gravity and friction, the acceleration of the object can be determined using the formula a = (mgsinθ - μmgcosθ) / m, where m is the mass of the object, g is the acceleration due to gravity, θ is the angle of the incline, and μ is the coefficient of friction.

What is the significance of the coefficient of friction in sliding down an incline?

The coefficient of friction is a crucial factor in determining the resistance between two surfaces in contact. In the case of sliding down an incline, the coefficient of friction affects the speed and acceleration of the object. A higher coefficient of friction means a greater resistance to motion, resulting in a slower descent of the object on the incline.

Similar threads

  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
18
Views
1K
  • Introductory Physics Homework Help
Replies
14
Views
2K
  • Introductory Physics Homework Help
Replies
32
Views
2K
  • Introductory Physics Homework Help
Replies
11
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
867
  • Introductory Physics Homework Help
Replies
33
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
13
Views
2K
Back
Top