A box with a mass of 7 kilograms is pushed up a ramp to a height of 5 meters. What is the work done against the force of gravity? Assume the ramp has negligible friction.
A. 3.4 x 10² joules
B. 6.9 x 10² joules
C. 8.6 x 10² joules
D. 1.7 x 10² joules
Answer (2)
The work done against gravity when pushing a 7 kg box up a 5-meter ramp is calculated using the formula W = mgh. This results in a value of 343 Joules, with the closest answer option being A (340 joules).
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The problem requires calculating the work done against gravity when lifting a box.
Use the formula W = m g h , where m = 7 kg, g = 9.8 m/s², and h = 5 m.
Substitute the values into the formula: W = 7 × 9.8 × 5 = 343 Joules.
The closest answer among the options is 3.4 × 1 0 2 joules .
Explanation
Understanding the Problem We are given a box with a mass of 7 kg that is pushed up a ramp to a height of 5 meters. We need to find the work done against the force of gravity. Since the ramp has negligible friction, all the work done is against gravity.
Identifying the Formula The work done against gravity is equal to the change in potential energy, which can be calculated using the formula: W = m g h where:
W is the work done (in Joules)
m is the mass of the box (in kg)
g is the acceleration due to gravity (approximately 9.8 m / s 2 )
h is the height the box is raised (in meters)
Substituting the Values Now, we substitute the given values into the formula: W = ( 7 kg ) × ( 9.8 m/s 2 ) × ( 5 m )
Calculating the Work Done Calculating the work done: W = 7 × 9.8 × 5 = 343 Joules
Selecting the Correct Answer Comparing our result with the given options: OA. 3.4 × 1 0 2 joules = 340 joules OB. 6.9 × 1 0 2 joules = 690 joules OC. 8.6 × 1 0 2 joules = 860 joules OD. 1.7 × 1 0 2 joules = 170 joules
The closest value to our calculated work done (343 Joules) is option A (340 Joules).
Final Answer Therefore, the work done against the force of gravity is approximately 340 Joules.
Examples
Imagine you're lifting a box onto a shelf. The work you do against gravity depends on the box's weight and how high you lift it. This concept is crucial in physics and engineering for calculating energy requirements in various scenarios, such as designing elevators, estimating the power needed to lift objects, or understanding energy expenditure in mechanical systems. By understanding the relationship between work, mass, gravity, and height, we can efficiently plan and execute tasks involving lifting objects.
