A 0.60 kg object with an initial velocity of 3.0 m/s in the positive x direction is acted on by a force in the direction of motion. The force does +2.5 J of work. What is the final velocity of the object?
KE = KE1 + KE2 = 0.5*M*V^2 + KE2 =
0.5*0.6*3^2 + 2.5 = 5.2 J.
KE = 0.5*0.6*V^2 = 5.2
V^2 = 17.33
V = 4.16 m/s.
A 0.60 kg Volleyball is moving with a intial velocity of 8 m/s and final velocity of 16 m/s. What is the total work done of this object? *
Well, if you have a 0.60 kg object moving at 3.0 m/s and it gets hit with a force doing +2.5 J of work, I bet it's feeling a bit woozy. It's like a fun game of bumper cars!
Now, to find the final velocity of the object, we can use the work-energy principle. The work done on an object is equal to the change in its kinetic energy. So we have:
Work = Change in Kinetic Energy
Since the initial kinetic energy is 0.5 * m * v_initial^2 and the final kinetic energy is 0.5 * m * v_final^2, we can rewrite the equation as:
Work = 0.5 * m * v_final^2 - 0.5 * m * v_initial^2
Now plug in the numbers:
2.5 J = 0.5 * 0.60 kg * v_final^2 - 0.5 * 0.60 kg * (3.0 m/s)^2
And after some calculations, you'll find that the final velocity of the object is approximately 3.56 m/s. So, it looks like our little bumper car got a pretty good boost!
To find the final velocity of the object, we can use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.
The equation for work is given by:
Work = Force x distance x cos(θ)
Since the force and displacement are in the same direction, cos(θ) equals 1. Hence, the equation simplifies to:
Work = Force x distance
Rearranging the equation, we can solve for the force:
Force = Work / distance
Given that the work done is +2.5 J, and the distance is not provided, we will assume the distance is 1 meter for simplicity.
Force = 2.5 J / 1 m
Force = 2.5 N
Using Newton's second law:
Force = mass x acceleration
Rearranging the equation, we can solve for acceleration:
Acceleration = Force / mass
Acceleration = 2.5 N / 0.60 kg
Acceleration = 4.17 m/s^2
Finally, we can use the kinematic equation to find the final velocity:
vf^2 = vi^2 + 2aΔx
Assuming the object starts from rest (initial velocity, vi = 0 m/s), and Δx = 1 m:
vf^2 = 0 + 2 * 4.17 m/s^2 * 1 m
vf^2 = 8.34 m^2/s^2
Taking the square root of both sides of the equation:
vf = √(8.34 m^2/s^2)
vf ≈ 2.89 m/s (rounded to two decimal places)
Therefore, the final velocity of the object is approximately 2.89 m/s.
To find the final velocity of the object, we need to use the work-energy principle. According to this principle, the work done on an object is equal to the change in its kinetic energy.
The work done on the object can be calculated using the formula:
Work = Force x Displacement x cos(theta)
In this case, the force is acting in the direction of motion, so the angle between the force and displacement is 0 degrees (cos(0) = 1). Therefore, we can simplify the formula as:
Work = Force x Displacement
Given that the work done on the object is +2.5 J, we know that:
2.5 J = Force x Displacement
Now, let's find the displacement of the object. Since the initial velocity is 3.0 m/s and the object is acted upon by a force, we can use the formula:
Displacement = (Final Velocity^2 - Initial Velocity^2) / (2 x Acceleration)
Assuming the object starts from rest and there is no acceleration other than the force acting on it, the formula becomes:
Displacement = (Final Velocity^2 - 3.0^2) / (2 x 0)
Here, we can see that the initial velocity will cancel out because we are subtracting it, and dividing by zero gives an undefined answer. This means the displacement is unknown from the given information.
Therefore, we cannot directly calculate the final velocity of the object. More information is needed, such as the displacement or any additional forces acting on the object during its motion.