fill in the blank ( Energy and momentum unit)
1. the work done to stretch a spring is not equal to the to force multiplied by displacement because force is ____ as the spring stretches
2. A child goes down a slide at the playground, gaining speed as she goes. Her momentum ____ because there is the presence of a(n) ____
no constant
the force increases as the spring stretches
F = k x
work = k x^2/2
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momentum increases
an external force, mg
1. The work done to stretch a spring is not equal to the force multiplied by displacement because force is not constant as the spring stretches. To understand why, we need to look at Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. Mathematically, this is expressed as F = k * x, where F is the force, k is the spring constant, and x is the displacement. Since the force changes as the spring stretches, we cannot simply multiply the force by the displacement to calculate the work done.
To calculate the work done to stretch a spring, we can use the integral of the force over the displacement. This involves finding the area under the force-displacement curve. By integrating the function F = k * x with respect to x, we can determine the work done.
2. A child goes down a slide at the playground, gaining speed as she goes. Her momentum increases because there is the presence of an external force. When an object experiences an external force, it can gain or lose momentum. In this case, as the child slides down the slide, the force of gravity acts on her, causing her to accelerate and gain speed. This acceleration leads to an increase in her momentum.
Momentum can be calculated using the equation p = m * v, where p is the momentum, m is the mass of the object, and v is the velocity. As the child gains speed while going down the slide, her velocity increases, which in turn increases her momentum. The presence of the external force (gravity, in this case) is crucial for the change in momentum. If there were no external force acting on the child, her momentum would remain constant throughout the slide.