An automobile traveling at 25km/hour has kinetic energy equal to 1x10 to the fourth power J. What is the mass of the car?
K.E. = (1/2)M V^2 = 10^4 J
Convert the speed to m/s and them use that V to solve for the mass of the car, in kg.
V = 25000 m/hr x (1 hr/3600 s) = _____ m/s
M = 2x(KE)/V^2 = ___ kg
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To solve for the mass of the car, we first need to convert the speed from kilometers per hour (km/hr) to meters per second (m/s):
V = 25 km/hr x (1000 m/1 km) x (1 hr/3600 s) = 6.94 m/s (rounded to two decimal places)
Next, we can use the formula for kinetic energy to solve for the mass (M) of the car:
K.E. = (1/2)M * V^2
Rearranging the formula, we get:
M = 2 * K.E. / V^2
Substituting the given values:
M = 2 * 10^4 J / (6.94 m/s)^2
Calculating the value in kg:
M ≈ 409.37 kg (rounded to two decimal places)
Therefore, the mass of the car is approximately 409.37 kg.
To find the mass of the car, we can start by converting the speed from kilometers per hour (km/hr) to meters per second (m/s).
Given:
K.E. = 1x10^4 J
V = 25 km/hr
First, we need to convert the speed from km/hr to m/s.
1 hour = 3600 seconds, therefore:
V = 25 km/hr x (1000 m/km) x (1 hr / 3600 s)
= (25,000 m / 3,600 s)
≈ 6.94 m/s (rounded to two decimal places)
Now, we can use the kinetic energy equation to find the mass of the car. The kinetic energy (K.E.) of an object is given by:
K.E. = (1/2)M V^2
Substituting the given values:
1x10^4 J = (1/2)M (6.94 m/s)^2
1x10^4 J = (1/2)M (48.07 m^2/s^2)
To solve for the mass (M), we rearrange the equation:
M = 2 x K.E. / V^2
M = 2 x (1x10^4 J) / (48.07 m^2/s^2)
M ≈ 414.85 kg (rounded to two decimal places)
Therefore, the mass of the car is approximately 414.85 kg.