Answer:
Force,
Explanation:
Given that,
A potential energy function for a system in which a two-dimensional force acts is of the form of :
We need to find the force that acts at the point (x, y). The force in 2 dimensional with components is given by :
So, the force acting at the point (x,y) is . Hence, this is the required solution.
Answer:
Final velocity at the bottom of hill is 15.56 m/s.
Explanation:
The given problem can be divided into four parts:
1. Use conservation of momentum to determine the speed of the combined mass (Gayle and sled)
From the law of conservation of momentum (perfectly inelastic collision), the combined velocity is given as:
2. Use conservation of energy to determine the speed after traveling a vertical height of 5 m.
The velocity of Gayle and sled at the instant her brother jumps on is found from the law of conservation of energy:
Here, initial velocity is the final velocity from the first stage. Therefore:
3. Use conservation of momentum to find the combined speed of Gayle and her brother.
Given:
Initial velocity of Gayle and sled is, m/s
Initial velocity of her brother is, m/s
Mass of Gayle and sled is, kg
Mass of her brother is, kg
Final combined velocity is given as:
m/s
4. Finally, use conservation of energy to determine the final speed at the bottom of the hill.
Using conservation of energy, the final velocity at the bottom of the hill is: