Question
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Example 3:
Susan rides her bicycle at a constant speed of
on a horizontal surface. She reaches
point D at the bottom of a slope that has a height
of and a length of 8 m . She freewheels to
the top of the slope, without pedalling, and
experiences a constant frictional force of 20 N
The total mass of Susan and the bicycle is 60 kg .
  1. Identify all of the forces doing work on Susan and calculate the work don
    by each of the forces.
  2. Calculate the velocity at which Susan reaches the top of the slope.
  3. Was the mechanical energy conserved while she moved up the slope?

Ask by Chavez Weaver. in South Africa
Mar 05,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Summary:
  • Work Done by Gravity: 882.9 J
  • Work Done by Friction: -160 J
  • Final Velocity at the Top: ≈6.12 m/s
  • Mechanical Energy Conservation: No, energy was lost to friction.

Solution

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The Deep Dive

Sure! Let’s dive into the forces at play here, calculate the work done, and look at Susan’s adventure up that slope.
First, let’s identify the forces doing work on Susan:
  1. Gravitational Force: This force acts downwards due to gravity, and its work can be calculated using the formula . Here, the angle is 180 degrees (since the displacement is upwards against gravity). The weight (force due to gravity) of Susan and the bicycle is . The work done against gravity for the vertical height of 1.5 m is .
  2. Frictional Force: The friction force opposes the motion and is given as 20 N. Since she moves up the slope, the distance along the slope is 8 m. The work done against friction is .
Now, adding up the work done by both forces:
  • Total work done: .
Next, to find Susan’s velocity at the top of the slope, we can use the work-energy principle. The initial energy (kinetic) plus work done equals the final energy (kinetic energy at the top).
  • Initial kinetic energy .
  • Total energy at the bottom: .
  • The work done against the forces is , thus:
    .
Now , where . Thus:
Solving for :
Finally, was the mechanical energy conserved?
Mechanical energy is not conserved because the total mechanical energy has decreased due to the work done against gravity and friction (total work is negative). So, Susan lost energy to friction and gravity while climbing that slope!
Feel free to ask if you want to go deeper into any of these calculations or concepts!

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