Work Done by Father on Girl's Sled Up Hill

In summary, the father does work by pushing his daughter's sled up a snowy incline with a constant velocity. The work done is equal to the sum of the x and y components, with the y component being calculated using the equation W=mgh. The final answer is 2300 J and can be found by converting the problem into a 1-d problem and calculating the distance and force parallel to the motion.
  • #1
colts2775
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Homework Statement



A father pushes horizontally on his daughter’s sled to move it up a snowy incline. If the sled moves up the hill with a constant velocity, how much work is done by the father in moving it from the bottom to the top of the hill? The angle is 15 degrees, the top of hill is 3.6 meters high, the mass of girl and sled is 35 kg, and the coefficient of kinetic friction is 0.20.

Homework Equations





The Attempt at a Solution



I know that you have to sum the x and y components, and I know the y component is W=mgh=(35kg)(9.8 m/s^2)(3.6 m), and I know the final answer is 2300 J but I don't know how to get there.
 
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  • #2
Work relates to the force parallel to the motion. Find that force first (i.e. turn the problem into a 1-d problem). Then find the distance of the motion. in this problem, it's easier that way... the motion is in a straight line against a constant force (caused by gravity in part and friction in part).
 
  • #3




To calculate the work done by the father on the sled, we can use the formula W = Fdcosθ, where F is the applied force, d is the displacement, and θ is the angle between the force and displacement vectors. In this case, the applied force is horizontal and the displacement is vertical, so the angle between them is 90 degrees. Therefore, the work done by the father can be calculated as:

W = Fd cos 90 = 0 J

This means that the father is not doing any work on the sled in the horizontal direction, as the sled is moving with a constant velocity. However, in the vertical direction, the father is working against the force of gravity and the frictional force. The work done against gravity can be calculated as W = mgh, where m is the mass of the sled and girl, g is the acceleration due to gravity, and h is the vertical displacement. Plugging in the given values, we get:

W = (35 kg)(9.8 m/s^2)(3.6 m) = 1272 J

The work done against friction can be calculated as W = Fd, where F is the frictional force and d is the horizontal displacement. The frictional force can be calculated as μmg, where μ is the coefficient of kinetic friction and mg is the weight of the sled and girl. Therefore, the work done against friction can be calculated as:

W = (0.20)(35 kg)(9.8 m/s^2)(3.6 m) = 254.4 J

Adding the work done against gravity and friction, we get the total work done by the father on the sled as:

W = 1272 J + 254.4 J = 1526.4 J

Therefore, the work done by the father on the sled from the bottom to the top of the hill is 1526.4 J.
 

1. What is the concept of "Work Done by Father on Girl's Sled Up Hill"?

The concept of "Work Done by Father on Girl's Sled Up Hill" refers to the physical exertion and energy required by a person (father) to push a sled carrying another person (girl) up a hill. This is a common scenario in activities such as sledding or skiing.

2. What factors affect the amount of work done by the father on the girl's sled up hill?

The amount of work done by the father on the girl's sled up hill is affected by several factors such as the weight of the sled and the girl, the steepness of the hill, and the friction between the sled and the snow. The father's strength and technique in pushing the sled also play a role.

3. Is the work done by the father on the girl's sled up hill a form of energy?

Yes, the work done by the father on the girl's sled up hill is a form of energy. When the father pushes the sled, he is transferring his potential energy (stored energy) into kinetic energy (energy of motion) to move the sled up the hill.

4. How is the work done by the father on the girl's sled up hill calculated?

The work done by the father on the girl's sled up hill can be calculated using the formula: W = F x d, where W is work (in joules), F is the force applied (in newtons), and d is the distance moved (in meters). The amount of work done is directly proportional to the force applied and the distance moved.

5. What is the significance of understanding the concept of "Work Done by Father on Girl's Sled Up Hill"?

Understanding the concept of "Work Done by Father on Girl's Sled Up Hill" can help us appreciate the physical effort and energy required in daily activities. It also helps us understand the principles of work and energy, and how they relate to real-life situations. Additionally, this concept has applications in fields such as physics, engineering, and sports.

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