A 70.0-kg runner has a speed of 5.90 m/s at one instant during a long-distance event.What is the runner's kinetic energy at this instant? If he doubles his speed to reach the finish line, by what factor does his kinetic energy change?
1. KE=0.5mV^2=0.5 * 70 * (5.90)^2=1218J
2. 2^2 = 4 = The factor by which the KE
is incrased.
To calculate the runner's kinetic energy at the given speed, we need to use the formula:
Kinetic Energy = (1/2) * m * v^2
Where:
m = mass of the runner = 70.0 kg
v = speed of the runner = 5.90 m/s
Plugging in the values, the kinetic energy at this instant can be calculated as:
Kinetic Energy = (1/2) * 70.0 kg * (5.90 m/s)^2
Kinetic Energy = 0.5 * 70.0 kg * 34.81 m^2/s^2
Kinetic Energy = 1216.35 Joules
Now, let's find the factor by which the kinetic energy changes when the runner doubles his speed.
The new speed after doubling is 5.90 m/s * 2 = 11.80 m/s.
Using the same formula as above, we can calculate the new kinetic energy:
Kinetic Energy (new) = (1/2) * m * v'^2
Where:
m = mass of the runner = 70.0 kg
v' = new speed of the runner = 11.80 m/s
Plugging in the values, the new kinetic energy can be calculated as:
Kinetic Energy (new) = (1/2) * 70.0 kg * (11.80 m/s)^2
Kinetic Energy (new) = 0.5 * 70.0 kg * 139.24 m^2/s^2
Kinetic Energy (new) = 4879.60 Joules
To find the factor by which the kinetic energy changes, we divide the new kinetic energy by the initial kinetic energy:
Factor = Kinetic Energy (new) / Kinetic Energy
Factor = 4879.60 Joules / 1216.35 Joules
Factor = 4.01
Therefore, the kinetic energy increases by a factor of 4.01 when the runner doubles his speed.
To calculate the runner's kinetic energy at a given instant, we can use the formula:
Kinetic Energy = (1/2) * mass * speed^2
Given:
Mass of the runner (m) = 70.0 kg
Speed of the runner (v) = 5.90 m/s
Substituting these values into the formula, we can calculate the kinetic energy:
Kinetic Energy = (1/2) * 70.0 kg * (5.90 m/s)^2
Kinetic Energy = 0.5 * 70.0 kg * (5.90 m/s)^2
Kinetic Energy = 0.5 * 70.0 kg * 34.81 m^2/s^2
Kinetic Energy = 1221.35 Joules
So, the runner's kinetic energy at this instant is 1221.35 Joules.
Now, let's calculate the change in kinetic energy when the runner doubles his speed.
The new speed becomes = 2 * 5.90 m/s = 11.80 m/s
Using the same formula, we can calculate the new kinetic energy:
New Kinetic Energy = (1/2) * 70.0 kg * (11.80 m/s)^2
New Kinetic Energy = 0.5 * 70.0 kg * 139.24 m^2/s^2
New Kinetic Energy = 4836.8 Joules
To find the factor by which the kinetic energy changes, we divide the new kinetic energy by the initial kinetic energy:
Factor = New Kinetic Energy / Initial Kinetic Energy
Factor = 4836.8 J / 1221.35 J
Factor ≈ 3.96
Therefore, when the runner doubles his speed, his kinetic energy increases by a factor of approximately 3.96.