In this problem, we are required to determine the force on an object given the position as a time-varying sine function.
Since we have the position as a function of time, we know this is a calculus problem.
A diagram like this one can help you remember the relationships between the variables:
We're looking for the force exerted on the object. That means we have to find an expression for acceleration, a(t). We'll obtain a(t) by differentiating the position function, x(t), twice then multiply it by the mass, m.
The steps needed to solve this problem are simple and straight forward:
In Step 1, we'll need to remember how to differentiate trigonometric functions.
Astronauts in space "weigh" themselves by oscillating on a spring. Suppose the position of an oscillating 76-kg astronaut is given by x = (0.31 m) sin((π rad/s)t), where t is in s.
(a) What force does the spring exert on the astronaut at t = 1.0 s? Note that the angle of the sine function is in radians.
(b) What force does the spring exert on the astronaut at t=1.5 s?
Frequently Asked Questions
What scientific concept do you need to know in order to solve this problem?
Our tutors have indicated that to solve this problem you will need to apply the Forces with Calculus concept. You can view video lessons to learn Forces with Calculus. Or if you need more Forces with Calculus practice, you can also practice Forces with Calculus practice problems.