Question

1. a. a boy carries a box with a weight of 70 n up a flight of stairs 20m high. how much potential energy has the box gained?

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1. b. a ball that has a mass of 6kg sits on a shelf that is 5m high. how much potential energy does the ball have?

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1. a. what is the mass of a box that has a potential energy of 20j sitting at the top of a hill that is 2m high?

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1. b. a toy with a weight of 8.5 n is on a shelf that is 25m high. how much potential energy does the toy have?

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1. a. a 75 kg box with a potential energy of 75j, is sitting on a table. what is the height of the box?

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1. b. what is the mass of a graduation cap with a potential energy of 25j, sitting 4m high on a shelf in the closet?

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Explanation:

1a

Step1: Identify the formula for potential energy

The formula for gravitational potential energy is \(PE = F\times h\) (where \(F\) is the force/weight and \(h\) is the height).

Step2: Substitute the given values

Given \(F = 70\ N\) and \(h=20\ m\). Then \(PE=70\times20\).

Step3: Calculate the result

\(PE = 1400\ J\)

Step1: Calculate the weight of the ball

First, find the weight \(F = mg\), where \(m = 6\ kg\) and \(g = 9.8\ m/s^{2}\). So \(F=6\times9.8=58.8\ N\).

Step2: Use the potential - energy formula

The formula for gravitational potential energy is \(PE = F\times h\). Substitute \(F = 58.8\ N\) and \(h = 5\ m\). Then \(PE=58.8\times5\).

Step3: Calculate the result

\(PE=294\ J\)

Step1: Rearrange the potential - energy formula for mass

From \(PE = mgh\), we can get \(m=\frac{PE}{gh}\). Given \(PE = 20\ J\), \(h = 2\ m\) and \(g = 9.8\ m/s^{2}\).

Step2: Substitute the values

\(m=\frac{20}{9.8\times2}\).

Step3: Calculate the result

\(m=\frac{20}{19.6}\approx1.02\ kg\)

Answer:

The box has gained \(1400\ J\) of potential energy.

1b