The force applied against an object moving horizontally on a linear path is described by #F(x)= cospix+x #. By how much does the object's kinetic energy change as the object moves from # x in [ 0, 2 ]#?
I got:
We can use the Work-K.E. theorem that tells us that:
or that work done on the system is equal to the change in kinetic energy.
Here we need to evaluate the work of a variable force so we use the integral version of work as:
So:
By signing up, you agree to our Terms of Service and Privacy Policy
To find the change in kinetic energy, integrate the force function F(x) over the interval [0, 2] to obtain the work done on the object. Then, use the work-energy principle, which states that the work done on an object equals the change in its kinetic energy. Finally, calculate the change in kinetic energy using the work done and the initial and final kinetic energies of the object.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- How much work would it take to push a # 25 kg # weight up a # 15 m # plane that is at an incline of # pi / 6 #?
- How much work is required? A motor of what power is required?
- A balanced lever has two weights on it, the first with mass #7 kg # and the second with mass #3 kg#. If the first weight is # 2 m# from the fulcrum, how far is the second weight from the fulcrum?
- What is the gravitational potential energy of a # 4 kg# object on a shelf # 3/5 m # high?
- An object with a mass of #8 kg# is hanging from an axle with a radius of #15 cm#. If the wheel attached to the axle has a radius of #90 cm#, how much force must be applied to the wheel to keep the object from falling?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7