Force of Friction: Solving for 15 kg Child on 4.0m Slide at 40 Degrees

In summary, a 15 kg child slides down a 4.0 m long playground slide at a 40 degree angle with the horizontal. The child's final speed is 3.2 m/s and the textbook states that the force of friction exerted by the slide on the child is 75N. However, using the equations of work and potential energy, the calculated force is 192.1 N, suggesting a discrepancy between the two answers. Further information on the velocity of the child may be needed to accurately solve for the force of friction.
  • #1
msimard8
57
0
This is my problem

A 15 kg child slides, from rest, down a playground slide tht is 4.0 m long, as shown in the figure. The slide makes a 40 degrees angle with the horizontal. The child's speed at the bottom is 3.2 m/s. What was teh force of friction that the sldie was exerting on the child?

Ok. The answer in the texbook says 75N.


Here is my WROng attempt

work=Kinetic Energy 2 - Kinetic Energy 1
work = 1/2 m (V2squared - v1squared)
w=1/2 (15 kg) (3.2 m/s squared - 0)
w=7.5 (10.24 m/s)
w=76.8 J

then I..

Work=force (distance) (cos40)
f= w/d (cos 40)
f=76.8 J / 4.0 (cos 40)
f=14.7 N

Where is my error.. HELP PLEASE
 
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  • #2
msimard8 said:
work=Kinetic Energy 2 - Kinetic Energy 1
work = 1/2 m (V2squared - v1squared)

w=1/2 (15 kg) (3.2 m/s squared - 0)
w=7.5 (10.24 m/s)
w=76.8 J
then I..
Work=force (distance) (cos40)
f= w/d (cos 40)
f=76.8 J / 4.0 (cos 40)
f=14.7 N
Where is my error.. HELP PLEASE
I've bolded the problem. Kinetic energy is not conserved, total energy is. That means that you must take potential energy into account.
 
  • #3
still no correct answer

I took what you said into effect. I still don't get 75 N as a result.

Given

m=15 kg
g=9.81m/s squared
final velocity=7.2 m/s
initial velocity = 0m/s
d=4.0 m

w= gravitational potential energy 1 - gravitational potential energy 2
w= [(m) (g) (h2)] - [(m) (g) (h1)]
w= mg (h2-h1)
w= 15 kg (9.81 m/s squared) (4.0m - 0)
w= 588.6 J


then

work = force (distance) (cos 40)
f=w/d cos 40
f= 588.6 J / 4.0 m (0.7660)
f= 588.6 J / 3.0641
f=192.1

therefore the answer is still wrong according to the textbook

How does Velocity relate to this problem?
 
Last edited:

1. What is the force of friction?

The force of friction is the resistance force that opposes the motion of an object when it comes into contact with another surface.

2. How do you calculate the force of friction?

The force of friction can be calculated using the formula F = μN, where F is the force of friction, μ is the coefficient of friction, and N is the normal force between the two surfaces.

3. What is the coefficient of friction?

The coefficient of friction is a dimensionless quantity that represents the ratio of the force of friction between two surfaces to the normal force pressing them together. It depends on the nature of the two surfaces in contact and their smoothness.

4. How do you solve for the force of friction in a specific scenario?

To solve for the force of friction in a specific scenario, you need to know the coefficient of friction between the two surfaces in contact and the normal force acting on the object. You can then use the formula F = μN to calculate the force of friction.

5. What is the importance of considering the force of friction in real-life situations?

The force of friction plays a crucial role in determining the motion and stability of objects in real-life situations. It helps us to understand how objects move, how to design machines and structures, and how to prevent accidents caused by friction.

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