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Tutor profile: Daryl P.

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Daryl P.
Physics Tutor
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Questions

Subject: Physics (Newtonian Mechanics)

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Question:

A person fires a projectile at an angle of $$ 15^{o} $$ above the horizontal, which hits the ground a certain distance down the range. For what other angle of launch at the same speed would the projectile land just as far away?

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Daryl P.
Answer:

To review, identical projectiles launched at complementary angles have the same range. Therefore, a projectile launched at $$ 15^{o} $$ will have the same range as a projectile launched at $$ 75^{o} $$.

Subject: Chemistry

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Question:

Balance the reaction for the complete combustion of pentane: $$ C_{5}H_{12} + O_{2} \rightarrow CO_{2} + H_{2}O $$

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Daryl P.
Answer:

In order to answer the question, we need to follow several steps: 1. Balance carbon. There's 5 carbon atoms so you need to match the $$ CO_{2} $$ with the same carbon atoms. $$ C_{5}H_{12} + O_{2} \rightarrow 5 CO_{2} + H_{2}O $$ 2. Balance hydrogen. There's 12 hydrogen atoms on the left so you need to match the $$ H_{2}O $$ with the same hydrogen atoms. $$ C_{5}H_{12} + O_{2} \rightarrow 5 CO_{2} + 6 H_{2}O $$ 3. Since you made adjustments with the carbon and hydrogen atoms, you need to adjust the oxygen atoms. So far, you have 10+6 oxygen atoms on the right, giving you a total of 16 oxygen atoms that you would need to balance out on the left. $$ C_{5}H_{12} + 8 O_{2} \rightarrow 5 CO_{2} + 6 H_{2}O $$ By putting 8 in $$ O_{2} $$, you now have 16 oxygen atoms on the left. If you would account for the carbon, hydrogen and oxygen atoms on both sides, you would find that they are already balanced out.

Subject: Physics

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Question:

A bolt connecting a shelf to a wall requires a torque of 15 Nm to tighten. If a 45 N force may be applied to a wrench in any given direction, what is the minimum length of the wrench that will result in the required torque?

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Daryl P.
Answer:

To answer the problem, you have to understand first what is torque. Simply put, torque is a measure of the force that can cause an object to rotate about an axis. To add, it is important to know that the placement of the force exerted to the wrench will impact the resulting torque. In the question, a 15 Nm torque is used to tighten a bolt with a force of 45 N. We would want to know the minimum length of the wrench that will result to a 15 Nm torque (we would assume also that the force is exerted at the far end of the wrench as opposed to the bolt). $$ \tau = F\cdot r $$ $$ r = \frac{\tau }{F} $$ $$ r = \frac{15 Nm }{45 N} $$ $$ r = 0.33 m $$ Therefore, the minimum length needed to result to a 15 Nm torque is 0.33 m long.

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