Kinetic energy = 1/2 mv^2 where m is the mass of the particle and v is the velocity of the particle. A joule is the SI unit for energy and is kg.m^2/s^2.
Find the energy in joules of a 56.7 g mass moving at the speed of 70. km. hr.
Convert 56.7 g t kg = 0.0567 kg.
Convert 70 km/hr to m/s = ?
Ke = 1/2 mv^2
To find the energy in joules, we need to convert the given mass and velocity into the appropriate units.
First, let's convert the mass from grams to kilograms.
56.7 g = 0.0567 kg
Next, let's convert the velocity from kilometers per hour to meters per second.
70 km/h = (70 * 1000) m/3600 s ≈ 19.444 m/s
Now, we can use the formula for kinetic energy:
Kinetic energy = 1/2 * mass * velocity^2
Plugging in the values we have:
Kinetic energy = 1/2 * 0.0567 kg * (19.444 m/s)^2
= 1/2 * 0.0567 kg * 378.024736 m^2/s^2
Simplifying the expression:
Kinetic energy ≈ 10.7686 kg.m^2/s^2
Since a joule is equal to a kilogram meter squared per second squared (kg.m^2/s^2), the energy in joules is approximately equal to 10.7686 J.
To find the energy in joules, we can use the formula for kinetic energy:
Kinetic energy (KE) = 1/2 * m * v^2
Given:
Mass (m) = 56.7 g = 0.0567 kg (since 1000 g = 1 kg)
Velocity (v) = 70 km/hr
First, let's convert the velocity from km/hr to m/s, since the SI unit for energy is kg.m^2/s^2.
To convert km/hr to m/s, we use the conversion factor of 1 km = 1000 m and 1 hr = 3600 s.
So, velocity in m/s = (70 km/hr) * (1000 m/km) * (1 hr/3600 s)
= (70 * 1000) / 3600
= 70000 / 3600
≈ 19.44 m/s
Now we have the mass (m) = 0.0567 kg and the velocity (v) = 19.44 m/s.
Plugging these values into the formula for kinetic energy:
KE = 1/2 * m * v^2
= 1/2 * 0.0567 kg * (19.44 m/s)^2
= 1/2 * 0.0567 kg * 378.05 m^2/s^2
≈ 4.27 joules
Therefore, the energy in joules of a 56.7 g mass moving at a speed of 70 km/hr is approximately 4.27 joules.