Set A
A1 Physics. The amount of deflection,
, of a plastic rod supported at
both ends under a load in the middle is
given by ,
where is the mass of the load.
(i) Find the deflection when a load of
200 g is added.
(ii) Explain if this model is suitable for
a load of 100 kg .

Ask by Savage Mullins. in Singapore

Mar 22,2025

Question

Set A
A1 Physics. The amount of deflection,
, of a plastic rod supported at
both ends under a load in the middle is
given by ,
where is the mass of the load.
(i) Find the deflection when a load of
200 g is added.
(ii) Explain if this model is suitable for
a load of 100 kg .

Ask by Savage Mullins. in Singapore

Mar 22,2025

UpStudy AI · Accepted Answer

Let's solve the problem step by step.

### Given:
The deflection $$ d $$ in mm is given by the equation:
$$
d = 0.002 m^2 + 0.02 m + 0.005
$$
where $$ m $$ is the mass of the load in grams.

### (i) Find the deflection when a load of 200 g is added.

1. Substitute $$ m = 200 $$ into the equation:
   $$
   d = 0.002(200^2) + 0.02(200) + 0.005
   $$

2. Calculate each term:
   - First term: $$ 0.002(200^2) $$
   - Second term: $$ 0.02(200) $$
   - Third term: $$ 0.005 $$

Let's calculate these values.
Calculate the value by following steps:
- step0: Calculate:
  $$0.02\times 200$$
- step1: Multiply the numbers:
  $$4$$
Calculate or simplify the expression $$ 0.002*(200^2) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$0.002\times 200^{2}$$
- step1: Rewrite the expression:
  $$0.002\times 40000$$
- step2: Multiply the numbers:
  $$80$$
Calculate or simplify the expression $$ 0.005 $$.
Numbers by following steps:
- step0: Solution:
  $$0.005$$
Now, let's calculate the deflection $$ d $$ using the computed values:

1. First term: $$ 0.002(200^2) = 80 $$
2. Second term: $$ 0.02(200) = 4 $$
3. Third term: $$ 0.005 $$

Now, we can sum these values to find $$ d $$:
$$
d = 80 + 4 + 0.005 = 84.005 \text{ mm}
$$

### (ii) Explain if this model is suitable for a load of 100 kg.

To determine if the model is suitable for a load of 100 kg, we need to convert the mass from kilograms to grams:
$$
100 \text{ kg} = 100,000 \text{ g}
$$

Now, we can substitute $$ m = 100,000 $$ into the original equation:
$$
d = 0.002(100000^2) + 0.02(100000) + 0.005
$$

Let's calculate this value to see if the model holds for such a large load.
Calculate the value by following steps:
- step0: Calculate:
  $$0.002\times 100000^{2}+0.02\times 100000+0.005$$
- step1: Multiply the numbers:
  $$2\times 10^{7}+0.02\times 100000+0.005$$
- step2: Multiply the numbers:
  $$2\times 10^{7}+2000+0.005$$
- step3: Add the numbers:
  $$2.0002\times 10^{7}$$
Calculating the deflection for a load of 100 kg gives us:
$$
d = 0.002(100000^2) + 0.02(100000) + 0.005 = 2.0002 \times 10^{7} \text{ mm}
$$

### Conclusion:
The deflection for a load of 100 kg is extremely large (20,002,000 mm or 20,002 m), which indicates that the model is not suitable for such a heavy load.

In practical terms, this suggests that the assumptions made in the model (such as linearity and material properties) may not hold true under such high loads, leading to unrealistic predictions of deflection.
When a 200 g load is applied, the deflection is 84.005 mm. For a 100 kg load, the deflection becomes extremely large (20,002,000 mm), making the model unsuitable for such heavy loads.

Set A
A1 Physics. The amount of deflection,
, of a plastic rod supported at
both ends under a load in the middle is
given by ,
where is the mass of the load.
(i) Find the deflection when a load of
200 g is added.
(ii) Explain if this model is suitable for
a load of 100 kg .

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Solución

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Set A A1 Physics. The amount of deflection, , of a plastic rod supported at both ends under a load in the middle is given by , where is the mass of the load. (i) Find the deflection when a load of 200 g is added. (ii) Explain if this model is suitable for a load of 100 kg .

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Physics Questions

Set A
A1 Physics. The amount of deflection,
, of a plastic rod supported at
both ends under a load in the middle is
given by ,
where is the mass of the load.
(i) Find the deflection when a load of
200 g is added.
(ii) Explain if this model is suitable for
a load of 100 kg .