A 15.0-kilogram mass is moving at 7.50 meters per second on a horizontal, frictionless surface. What is the
total work that must be done on the mass to increase its speed to 11.5 meters per second?
570J is the correct answer
work done = change in kinetic energy
= (1/2) (15)(11.5^2 - 7.5^2)
To find the total work done on the mass to increase its speed, we need to calculate the change in kinetic energy.
The formula for kinetic energy is KE = (1/2) * mass * velocity^2.
First, let's calculate the initial kinetic energy (KE_initial) of the mass:
KE_initial = (1/2) * mass * velocity_initial^2
where mass = 15.0 kg and velocity_initial = 7.50 m/s.
KE_initial = (1/2) * 15.0 kg * (7.50 m/s)^2
Next, let's calculate the final kinetic energy (KE_final) of the mass:
KE_final = (1/2) * mass * velocity_final^2
where velocity_final = 11.5 m/s.
KE_final = (1/2) * 15.0 kg * (11.5 m/s)^2
Now, we can calculate the change in kinetic energy (ΔKE):
ΔKE = KE_final - KE_initial
Substitute the values into the equation:
ΔKE = [(1/2) * 15.0 kg * (11.5 m/s)^2] - [(1/2) * 15.0 kg * (7.50 m/s)^2]
Simplify the equation:
ΔKE = [0.5 * 15.0 kg * (11.5 m/s)^2] - [0.5 * 15.0 kg * (7.50 m/s)^2]
Now, calculate the value of ΔKE.
Finally, the total work done is equal to the change in kinetic energy:
Total work = ΔKE
Calculate the final result to find the total work done on the mass to increase its speed.