A skier with a potential energy of [tex]$137,200 J$[/tex] waits on top of a ski jump that is 200 m high. What is the mass of the skier?
A. 20 kg
B. 70 kg
C. 137 kg
D. 686 kg
Answer (2)
The mass of the skier can be calculated using the potential energy formula, which gives us a mass of 70 kg after substituting the given values. Therefore, the answer is B. 70 kg.
;
Use the potential energy formula: PE = m g h .
Rearrange the formula to solve for mass: m = g h PE .
Substitute the given values: m = 9.8 × 200 137200 .
Calculate the mass: m = 70 k g . The mass of the skier is 70 k g .
Explanation
Understanding the Problem We are given the potential energy of a skier at the top of a ski jump and the height of the jump. We need to find the mass of the skier.
Recalling the Potential Energy Formula We know that the potential energy (PE) is given by the formula: PE = m g h where:
m is the mass of the object (in kg),
g is the acceleration due to gravity (approximately 9.8 m / s 2 ),
h is the height of the object above the ground (in meters).
Identifying Given Values We are given:
PE = 137 , 200 J
h = 200 m
g = 9.8 m / s 2 We need to find m .
Rearranging the Formula We can rearrange the formula to solve for m :
m = g h PE
Substituting the Values and Calculating Now, we substitute the given values into the formula: m = 9.8 × 200 137200 m = 1960 137200 m = 70
Final Answer Therefore, the mass of the skier is 70 kg.
Examples
Potential energy is a fundamental concept in physics. Imagine a roller coaster at the highest point of its track. The roller coaster has maximum potential energy at this point, which converts to kinetic energy as it descends. Knowing the potential energy, height, and gravitational acceleration, we can determine the mass of the roller coaster. This principle is used in various applications, such as designing efficient transportation systems and understanding energy storage.
