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In the 2011 film Fast Five, the fast five steal a bank vault. A quick search gives the average mass of a bank vault to be in the area of 45,000 𝑘𝑔. In the film, they’re pulling with a couple of Dodge Chargers, which, despite having serious horsepower, have a relatively low towing capacity of 453 𝑘𝑔 each. There’s no way these will do the job, but let’s pretend they can. The coefficients of static and kinetic friction between steel (for the vault) and concrete (for the road) are 𝜇𝑠 = 0.65 and 𝜇𝑘 = 0.40 . Of course, the crew doesn’t necessarily think everything through, so they affix their cables at a downward angle of 10∘, as shown. a. How much force does it take to get the vault moving? Just a bit later, they turn a corner while towing this vault. The cables they’re using have a length of 20 𝑚 and they’re moving at a speed of 30 𝑚𝑝h (13.4 𝑚⁄𝑠) as they take the turn. For this part, don’t worry about the angle in the rope; we’ll assume things have slipped a bit and the rope is now horizontal. You can also assume that the frictional force during this turn is in its most helpful orientation, so take friction to point in the same direction as tension. b. How much tension in the cable?

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Answer to a math question In the 2011 film Fast Five, the fast five steal a bank vault. A quick search gives the average mass of a bank vault to be in the area of 45,000 𝑘𝑔. In the film, they’re pulling with a couple of Dodge Chargers, which, despite having serious horsepower, have a relatively low towing capacity of 453 𝑘𝑔 each. There’s no way these will do the job, but let’s pretend they can. The coefficients of static and kinetic friction between steel (for the vault) and concrete (for the road) are 𝜇𝑠 = 0.65 and 𝜇𝑘 = 0.40 . Of course, the crew doesn’t necessarily think everything through, so they affix their cables at a downward angle of 10∘, as shown. a. How much force does it take to get the vault moving? Just a bit later, they turn a corner while towing this vault. The cables they’re using have a length of 20 𝑚 and they’re moving at a speed of 30 𝑚𝑝h (13.4 𝑚⁄𝑠) as they take the turn. For this part, don’t worry about the angle in the rope; we’ll assume things have slipped a bit and the rope is now horizontal. You can also assume that the frictional force during this turn is in its most helpful orientation, so take friction to point in the same direction as tension. b. How much tension in the cable?

Expert avatar
Santino
4.5
110 Answers
**Part A: Force to Get the Vault Moving**

Given:
- Mass of the vault, m = 45,000 \, \text{kg}
- Gravitational acceleration, g = 9.81 \, \text{m/s}^2
- Coefficient of static friction, \mu_s = 0.63

Normal force, N = m \cdot g = 45,000 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 = 441,450 \, \text{N}

Force of static friction, F_{\text{static}} = \mu_s \cdot N = 0.63 \cdot 441,450 \, \text{N} = 278,567.5 \, \text{N}

**Answer: The force required to get the vault moving is 278,567.5 \, \text{N}.

**Part B: Tension in the Cable While Turning**

Given:
- Speed, v = 13.4 \, \text{m/s}
- Radius, r = 20 \, \text{m}

Centripetal force required, F_{\text{centripetal}} = \frac{m \cdot v^2}{r} = \frac{45,000 \, \text{kg} \cdot (13.4 \, \text{m/s})^2}{20 \, \text{m}} = 404,010.0 \, \text{N}

The tension in the cable while turning is approximately 404,010.0 \, \text{N}.

**Answer: The tension in the cable while turning is 404,010.0 \, \text{N}.

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