Question

When a car decelerates, a spider, hanging from a length of webbing, shifts forward to create a 25 degree angle with the vertical. The spider has a mass of 10 grams. Using this information, what is the deceleration of the vehicle?

Answer 1

Answer on Question #82186 Physics / Mechanics | Relativity

When a car decelerates, a spider, hanging from a length of webbing, shifts forward to create a 25 degree angle with the vertical. The spider has a mass of 10 grams. Using this information, what is the deceleration of the vehicle?

Solution:

The Newton's second law gives

$$m \mathbf {a} = m \mathbf {g} + \mathbf {T}$$

In projections on the axes

$$m a = T \sin 2 5 {}^ {\circ}$$ $$0 = m g - T \cos 2 5 {}^ {\circ}$$

Finally

$$a = g \tan 2 5 {}^ {\circ} = 9. 8 1 \times \tan 2 5 {}^ {\circ} = 4. 5 7 \mathrm {m / s ^ {2}}$$

Answer: $4.57 \, \text{m/s}^2$

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