Mass on Inclined Plane with Friction

In summary, a block of mass M = 2.5 kg slides down an incline with an angle of 31° with the horizontal and a coefficient of kinetic friction of 0.2. The block's acceleration is 3.37 m/s^2 and the work done on the block by the Earth's gravitational force is 75.7878 N-m. The amount of energy expended in overcoming frictional force is unknown and the kinetic energy of the block is also unknown. The normal force exerted by the plane on the block does no work. The distance d = 6 m is given for the subsequent four questions.
  • #1
r34racer01
63
0
A block of mass M = 2.5 kg is released from rest and slides down an incline that makes an angle q = 31° with the horizontal. The coefficient of kinetic friction between the block and the incline is µk = 0.2.

a) What is the acceleration of the block down the inclined plane?
I got a = 3.37

The next four questions are concerned with what has happened after the block slides a distance d = 6 m down the plane.

b) How much work was done on the block by the Earth's gravitational force?
I got Wg = 75.7878

c) How much energy was expended in overcoming the frictional force (thus producing heat, etc.)?

d) What is the kinetic energy of the block?

e) The plane exerts a normal force (perpendicular to its surface) on the block. How much work was done on the block by this normal force?
Easy that's 0.

I just can't get how to get E-heat or KE?

Homework Statement


Homework Equations


The Attempt at a Solution

 
Last edited:
Physics news on Phys.org
  • #2
r34racer01 said:
A block of mass M = 2.5 kg is released from rest and slides down an incline that makes an angle q = 31° with the horizontal. The coefficient of kinetic friction between the block and the incline is µk = 0.2.

a) What is the acceleration of the block down the inclined plane?
I got a = 3.37

b) How much work was done on the block by the Earth's gravitational force?
I got Wg = 75.7878

c) How much energy was expended in overcoming the frictional force (thus producing heat, etc.)?

d) What is the kinetic energy of the block?

e) The plane exerts a normal force (perpendicular to its surface) on the block. How much work was done on the block by this normal force?
Easy that's 0.

I just can't get how to get E-heat or KE?

Homework Statement



Homework Equations



The Attempt at a Solution


Let me guess there is a distance given in a figure that you haven't provided? Work is N-m and I'm not seeing any meters.
 
  • #3
LowlyPion said:
Let me guess there is a distance given in a figure that you haven't provided? Work is N-m and I'm not seeing any meters.

Ah, no I've given everything.
 
  • #4
r34racer01 said:
Ah, no I've given everything.

Ok then what is the distance?
 
  • #5
LowlyPion said:
Ok then what is the distance?

Oh my bad I didn't see that after pt a they say

"The next four questions are concerned with what has happened after the block slides a distance d = 6 m down the plane."

Sorry about that.
 
  • #6
r34racer01 said:
Oh my bad I didn't see that after pt a they say

"The next four questions are concerned with what has happened after the block slides a distance d = 6 m down the plane."

Sorry about that.

OK then what was the term that you used for determining the friction in calculating the acceleration? It is that force acting over the distance that will be the work done by friction.
 
  • #7
LowlyPion said:
OK then what was the term that you used for determining the friction in calculating the acceleration? It is that force acting over the distance that will be the work done by friction.

Well what I did was F = ma, in this case (mg sin 31) - Ff = ma.
So ((2.5*9.81) sin 31) - (0.2(2.5*9.81 cos 31) = 2.5*a = 3.37
To determine friction I just calculated the normal force * uk. In terms of forces they act over the distance but not in terms of work at least for normal force.
 
  • #8
r34racer01 said:
Well what I did was F = ma, in this case (mg sin 31) - Ff = ma.
So ((2.5*9.81) sin 31) - (0.2(2.5*9.81 cos 31) = 2.5*a = 3.37
To determine friction I just calculated the normal force * uk. In terms of forces they act over the distance but not in terms of work at least for normal force.

Friction does act over that distance however. While its scalar magnitude is a function of the normal force its direction of action is parallel to the incline. Hence the frictional force component times distance does have a non zero contribution to work - albeit negative.
 

1. What is a mass on inclined plane with friction?

A mass on inclined plane with friction is a classic physics problem that involves a block or object placed on a sloped surface, with the inclusion of friction. It is commonly used to understand the effects of gravity and friction on an object's motion.

2. How is the acceleration of the mass calculated?

The acceleration of the mass on an inclined plane with friction can be calculated using the following formula: a = g(sinθ - μcosθ), where g is the acceleration due to gravity, θ is the angle of the inclined plane, and μ is the coefficient of friction between the object and the surface.

3. What is the significance of the coefficient of friction in this problem?

The coefficient of friction is a measure of the amount of resistance an object experiences when moving over a surface. In the context of a mass on an inclined plane, it determines the amount of force needed to overcome the friction and move the object along the slope.

4. How does the angle of the inclined plane affect the motion of the mass?

The angle of the inclined plane has a direct impact on the acceleration of the mass. As the angle increases, the acceleration increases, reaching a maximum when the angle is 90 degrees. This is because a steeper slope requires a greater force to overcome the effects of gravity and friction.

5. What are some real-world applications of this problem?

The concept of a mass on an inclined plane with friction has various practical applications, such as understanding the motion of objects on ramps and hills, predicting the movement of vehicles on curved roads, and analyzing the motion of skiers on slopes. It is also used in industries such as construction and transportation to design and optimize structures and vehicles for efficient movement.

Similar threads

  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
27
Views
5K
  • Introductory Physics Homework Help
Replies
33
Views
2K
  • Introductory Physics Homework Help
Replies
30
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
2K
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
12
Views
1K
  • Introductory Physics Homework Help
Replies
19
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
929
  • Introductory Physics Homework Help
Replies
3
Views
2K
Back
Top