- #1

lpettigrew

- 115

- 10

- Homework Statement
- Hello, in each of the following a physical problem is given alongside a mathematical model. I have been tasked with deciding whether the model is a good one and suggesting possible improvements.

1) A ball is thrown vertically upwards. Find the time before it gets to its greatest height.

Mathematical model; The tennis ball is modelled as a particle moving under constant gravity with no air resistance.

2. In a game of ice hockey, the puck is hit towards the goal. Find the time it takes to reach the goalkeeper.

Mathematical model; The puck is modelled as a particle moving on a smooth surface.

3. A cart is pulled forward by two horses. Find the tensions in the ropes assuming it is moving with constant speed.

Mathematical Model; The horses and cart are assumed to be particles, the string is assumed to be inextensible and horizontal and there is no resistance in the moving parts of the cart.

- Relevant Equations
- 1) A ball is thrown vertically upwards. Find the time before it gets to its greatest height.

2. In a game of ice hockey, the puck is hit towards the goal. Find the time it takes to reach the goalkeeper.

3. A cart is pulled forward by two horses. Find the tensions in the ropes assuming it is moving with constant speed.

I am really struggling with these problems and do not really know where to begin. In most cases I have just defined what the modelling means, e.g A rough surface is one upon which friction acts etc.

I would really appreciate some help with suitably answering these questions comprehensively, and would note that the textbook I found them in states that each is worth 4 marks, yet I certainly have even unable to make four solid points.

Thank you to anyone who takes the time to offer help and guidance

1) A ball is thrown vertically upwards. Find the time before it gets to its greatest height.

Mathematical model; The tennis ball is modeled as a particle moving under constant gravity with no air resistance.

I know that when an object moves freely under gravity, one can ignore air resistance, which also means that acceleration is constant.

However, the tennis ball in not freely falling since it is accelerating upwards, nor is acceleration constant, so it cannot be assumed that air resistance is negligible.

However, since the ball is modeled as a particle this a fitting analogy and means that when modelling something as a particle, the mass of the object acts through a single point i.e. the size of the object is irrelevant. The particle has no dimensions which means that resistive forces due to e.g. rotation or air resistance can be ignored.2. In a game of ice hockey, the puck is hit towards the goal. Find the time it takes to reach the goalkeeper.

Mathematical model; The puck is modeled as a particle moving on a smooth surface.

Yes, I believe that this is a good model since it would be safe to assume that the puck experiences no friction on the ice, i.e. we could treat the ice as smooth in this case. A smooth surface is frictionless.

3. A cart is pulled forward by two horses. Find the tensions in the ropes assuming it is moving with constant speed.

Mathematical Model; The horses and cart are assumed to be particles, the string is assumed to be inextensible and horizontal and there is no resistance in the moving parts of the cart.

An inextensible string is a string which has a fixed length, it is impossible to stretch, so this statement is appropriate here. Moreover, the depiction of the horses and cart as particles means that mass of the objects acts through a single point and thus the particles do not have resistive forces due to e.g. air resistance. This agrees with the statement that there is no resistance in the moving parts of the cart.

Would an improvement be to assume that the string in light, i.e. it has no mass so no weight acts on a light body?

I would really appreciate some help with suitably answering these questions comprehensively, and would note that the textbook I found them in states that each is worth 4 marks, yet I certainly have even unable to make four solid points.

Thank you to anyone who takes the time to offer help and guidance

1) A ball is thrown vertically upwards. Find the time before it gets to its greatest height.

Mathematical model; The tennis ball is modeled as a particle moving under constant gravity with no air resistance.

I know that when an object moves freely under gravity, one can ignore air resistance, which also means that acceleration is constant.

However, the tennis ball in not freely falling since it is accelerating upwards, nor is acceleration constant, so it cannot be assumed that air resistance is negligible.

However, since the ball is modeled as a particle this a fitting analogy and means that when modelling something as a particle, the mass of the object acts through a single point i.e. the size of the object is irrelevant. The particle has no dimensions which means that resistive forces due to e.g. rotation or air resistance can be ignored.2. In a game of ice hockey, the puck is hit towards the goal. Find the time it takes to reach the goalkeeper.

Mathematical model; The puck is modeled as a particle moving on a smooth surface.

Yes, I believe that this is a good model since it would be safe to assume that the puck experiences no friction on the ice, i.e. we could treat the ice as smooth in this case. A smooth surface is frictionless.

3. A cart is pulled forward by two horses. Find the tensions in the ropes assuming it is moving with constant speed.

Mathematical Model; The horses and cart are assumed to be particles, the string is assumed to be inextensible and horizontal and there is no resistance in the moving parts of the cart.

An inextensible string is a string which has a fixed length, it is impossible to stretch, so this statement is appropriate here. Moreover, the depiction of the horses and cart as particles means that mass of the objects acts through a single point and thus the particles do not have resistive forces due to e.g. air resistance. This agrees with the statement that there is no resistance in the moving parts of the cart.

Would an improvement be to assume that the string in light, i.e. it has no mass so no weight acts on a light body?