A 0.5 kg block initially at rest on a frictionless, horizontal surface is acted upon by a force of 5.0 N for a distance of 4.0 m. How much kinetic energy does the block gain? What is its final velocity?
mass=0.5 kg
force=5 N
f=ma
a=force/mass
a=5/0.5
a=10m/s^2
u=0
s=4m
v^2-u^2=2as
v^2=2*10*4
v^2=80
final velocity = v = 8.9m/s
kinetic energy = 0.5*m*v^2=0.5*0.5*80
=20
gain in kinetic energy= final kinetic energy -initial kinetic energy
=20-0=20
To find the amount of kinetic energy gained by the block, we can use the work-energy theorem. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.
The formula for work is given by W = F * d * cos(theta), where W is the work done, F is the force applied, d is the distance over which the force is applied, and theta is the angle between the force vector and the displacement vector.
In this case, the block is on a frictionless surface, so there is no angle between the force and displacement vectors. This means cos(theta) = 1, so we can simplify the formula to W = F * d.
The block is acted upon by a force of 5.0 N over a distance of 4.0 m. Plugging these values into the formula, we have:
W = 5.0 N * 4.0 m = 20 J
The work done on the block is 20 J. According to the work-energy theorem, this is equal to the change in kinetic energy of the block.
Therefore, the block gains 20 J of kinetic energy.
To find the final velocity of the block, we can use the equation for the kinetic energy of an object:
KE = 0.5 * m * v^2
Where KE is the kinetic energy, m is the mass of the object, and v is its velocity.
We already know that the block gains 20 J of kinetic energy, and we are given the mass of the block as 0.5 kg. Plugging these values into the equation, we have:
20 J = 0.5 * 0.5 kg * v^2
We can solve this equation to find the final velocity of the block:
40 = 0.5 * v^2
Dividing both sides by 0.5, we get:
80 = v^2
Taking the square root of both sides, we find:
v = √80 ≈ 8.9 m/s
Therefore, the block gains 20 J of kinetic energy and its final velocity is approximately 8.9 m/s.