A motorcycle weighs 2,009 newtons. The mass of the motorcycle is _______ kilograms. Use g = 9.8 N/kg for gravity.
Answer (2)
The mass of the motorcycle is approximately 205 kilograms, calculated using the formula m = g W . By substituting the values, we find m = 9.8 2009 ≈ 205 kg .
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The problem provides the weight of a motorcycle (2009 N) and the acceleration due to gravity (9.8 N/kg).
We use the formula W = m × g to relate weight, mass, and gravity.
Rearrange the formula to solve for mass: m = g W .
Substitute the given values and calculate: m = 9.8 2009 ≈ 205 kg . The mass of the motorcycle is approximately 205 kilograms.
Explanation
Understanding the Problem We are given the weight of a motorcycle, which is 2009 Newtons, and the acceleration due to gravity, which is 9.8 N/kg. We need to find the mass of the motorcycle in kilograms.
Stating the Formula The formula that relates weight, mass, and gravity is: W e i g h t = ma ss × g r a v i t y or W = m × g
Rearranging the Formula We need to rearrange the formula to solve for mass: ma ss = g r a v i t y W e i g h t or m = g W
Substituting the Values Now, we substitute the given values into the formula: m = 9.8 N/kg 2009 N
Calculating the Mass Performing the calculation: m = 9.8 2009 ≈ 205 kg
Final Answer Therefore, the mass of the motorcycle is approximately 205 kilograms.
Examples
Understanding the relationship between weight, mass, and gravity is crucial in many real-world scenarios. For example, when designing bridges or buildings, engineers need to calculate the weight of the materials they will be using. This calculation requires knowing the mass of the materials and the acceleration due to gravity. Similarly, when launching a rocket into space, scientists need to account for the changing acceleration due to gravity as the rocket moves further away from the Earth. This requires a precise understanding of the relationship between weight, mass, and gravity.
