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2. A mass my creates a gravitational field. Use the diagram below to answer the following questions. Position vector defines a location of interest. |F| = 136 m MA = 3.2x10¹4 kg 679 TLA Chosen coordinate System - 5 a) Put the position vector into component form, using the given Cartesian coordinate system. Show all steps to receive full credit. b) Find the unit vector f that describes the direction of the position vector. Show all steps to receive full credit. c) Find the norm of the unit vector f that you just found in (b). Show all steps. (If you don't get an answer very close to 1, go back to (b) and try again.) d) Find the gravitational field vector generated by mĄ at the location of interest, in component form. Don't forget units. e) Draw the direction of the gravitational field vector gĄ, that you found in (d).

2. A mass my creates a gravitational field. Use the diagram below to answer the following questions. Position vector defines a location of interest. |F| = 136 m MA = 3.2x10¹4 kg 679 TLA Chosen coordinate System - 5 a) Put the position vector into component form, using the given Cartesian coordinate system. Show all steps to receive full credit. b) Find the unit vector f that describes the direction of the position vector. Show all steps to receive full credit. c) Find the norm of the unit vector f that you just found in (b). Show all steps. (If you don't get an answer very close to 1, go back to (b) and try again.) d) Find the gravitational field vector generated by mĄ at the location of interest, in component form. Don't forget units. e) Draw the direction of the gravitational field vector gĄ, that you found in (d).

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**Problem 2: Gravitational Field Analysis** A mass \(m_A\) creates a gravitational field. Use the diagram below to answer the following questions. Position vector \(\vec{r}\) defines a location of interest. Given: - \(|\vec{r}| = 136 \, \text{m}\) - \(m_A = 3.2 \times 10^{14} \, \text{kg}\) **Diagram Description:** - The diagram shows a position vector \(\vec{r}\) at an angle of 67° from the negative x-axis towards the negative y-axis. - \(m_A\) is located at the origin of the coordinate system. **Coordinate System:** - Positive \(x\) direction points to the left. - Positive \(y\) direction points upwards. - Positive \(z\) direction points out of the page. **Questions:** a) **Component Form of \(\vec{r}\):** Put the position vector into component form using the given Cartesian coordinate system. Show all steps to receive full credit. b) **Unit Vector \(\hat{r}\):** Find the unit vector \(\hat{r}\) that describes the direction of the position vector. Show all steps to receive full credit. c) **Norm of Unit Vector \(\hat{r}\):** Find the norm of the unit vector \(\hat{r}\) that you just found in (b). Show all steps. (If you don’t get an answer very close to 1, go back to (b) and try again.) d) **Gravitational Field Vector \(\vec{g}_A\):** Find the gravitational field vector \(\vec{g}_A\) generated by \(m_A\) at the location of interest, in component form. Don’t forget units. e) **Direction of \(\vec{g}_A\):** Draw the direction of the gravitational field vector \(\vec{g}_A\) that you found in (d).
Transcribed Image Text:**Problem 2: Gravitational Field Analysis** A mass \(m_A\) creates a gravitational field. Use the diagram below to answer the following questions. Position vector \(\vec{r}\) defines a location of interest. Given: - \(|\vec{r}| = 136 \, \text{m}\) - \(m_A = 3.2 \times 10^{14} \, \text{kg}\) **Diagram Description:** - The diagram shows a position vector \(\vec{r}\) at an angle of 67° from the negative x-axis towards the negative y-axis. - \(m_A\) is located at the origin of the coordinate system. **Coordinate System:** - Positive \(x\) direction points to the left. - Positive \(y\) direction points upwards. - Positive \(z\) direction points out of the page. **Questions:** a) **Component Form of \(\vec{r}\):** Put the position vector into component form using the given Cartesian coordinate system. Show all steps to receive full credit. b) **Unit Vector \(\hat{r}\):** Find the unit vector \(\hat{r}\) that describes the direction of the position vector. Show all steps to receive full credit. c) **Norm of Unit Vector \(\hat{r}\):** Find the norm of the unit vector \(\hat{r}\) that you just found in (b). Show all steps. (If you don’t get an answer very close to 1, go back to (b) and try again.) d) **Gravitational Field Vector \(\vec{g}_A\):** Find the gravitational field vector \(\vec{g}_A\) generated by \(m_A\) at the location of interest, in component form. Don’t forget units. e) **Direction of \(\vec{g}_A\):** Draw the direction of the gravitational field vector \(\vec{g}_A\) that you found in (d).
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