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Marysya12 [62]
3 years ago
14

3. An object with a mass of 10 kg is moving along a horizontal surface. At a certain point it has 40 J of kinetic energy. If the

coefficient of friction between the object and the surface is 0.40, how far will the object go beyond that point before coming to a stop? Use g = 10 m/s2
Physics
1 answer:
damaskus [11]3 years ago
7 0

Answer: 100cm

Explanation:

The force of friction on a surface normal to gravity where µ is the coefficient of friction is

F = µmg

Where

F = the friction force

µ = coefficient of friction

m = mass of the object

g = acceleration due to gravity

Also, the Kinetic Energy of the object, E = Fs, where

E = Kinetic Energy

s = stopping distance. So that,

E = µmgs

40 J = 0.4 * 10 kg * 10 m/s² * s

40 J = 40 kgm/s² * s

s = 40 J / 40 kgm/s²

s = 1 m or 100 cm

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Traveling 221 miles from Boston Back Bay Station to NYC Penn Station takes 3 hours
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Answer:

Approximately 116\; \text{miles} for the train from Boston to NYC Penn Station.

Approximately 105\; \text{miles} for the train from NYC Penn Station to Boston.

Explanation:

Convert minutes to hours:

\begin{aligned}t(\text{BOS $\to$ NYC}) &= 3\; {\text{hour}} + 40\; \text{minute} \times \frac{1\; {\text{hour}}}{60\; \text{minute}} \\ &=\left(3 + \frac{2}{3}\right)\; \text{hour}\\ &= \frac{11}{3}\; \text{hour} \end{aligned}.

\begin{aligned}t(\text{NYC $\to$ BOS}) &= 4\; {\text{hour}} + 5\; \text{minute} \times \frac{1\; {\text{hour}}}{60\; \text{minute}} \\ &= \frac{49}{15}\; \text{hour} \end{aligned}.

Calculate average speed of each train:

\begin{aligned}v(\text{BOS $\to$ NYC}) &= \frac{s}{t}\\ &= \frac{221\; \text{mile}}{\displaystyle \frac{11}{3}\; \text{hour}} \\ &= \frac{663}{11}\; \text{mile} \cdot \text{hour}^{-1}\end{aligned}.

\begin{aligned}v(\text{NYC $\to$ BOS}) &= \frac{s}{t}\\ &= \frac{221\; \text{mile}}{\displaystyle \frac{49}{15}\; \text{hour}} \\ &= \frac{2652}{49}\; \text{mile} \cdot \text{hour}^{-1}\end{aligned}

Assume that it takes a time period of t for the trains to pass by each other after departure. Distance each train travelled would be:

s(\text{NYC $\to$ BOS}) = v(\text{NYC $\to$ BOS})\, t.

s(\text{BOS $\to$ NYC}) = v(\text{BOS $\to$ NYC})\, t.

Since the trains have just passed by each other, the sum of the two distances should be equal to the distance between the stations:

v(\text{NYC $\to$ BOS})\, t + v(\text{BOS $\to$ NYC})\, t = 221\; \text{mile}.

Rearrange and solve for t:

(v(\text{NYC $\to$ BOS}) + v(\text{BOS $\to$ NYC}))\, t = 221\; \text{mile}.

\begin{aligned}t &= \frac{221\; \text{mile}}{v(\text{NYC $\to$ BOS}) + v(\text{BOS $\to$ NYC})} \\ &= \frac{221\; \text{mile}}{\displaystyle \frac{663}{11}\; \text{mile} \cdot \text{hour}^{-1} + \frac{2652}{49}\; \text{mile} \cdot \text{hour}^{-1}} \\ &= \frac{539}{279}\; \text{hour}\end{aligned}.

Distance each train travelled in t = (539 / 279)\; \text{hour}:

\begin{aligned}s(\text{BOS $\to$ NYC}) &= v\, t \\ &= \frac{663}{11}\; \text{mile} \cdot \text{hour}^{-1} \times \frac{539}{279}\; \text{hour} \\ &\approx 116\; \text{mile}\end{aligned}.

\begin{aligned}s(\text{NYC $\to$ BOS}) &= v\, t \\ &= \frac{2652}{49}\; \text{mile} \cdot \text{hour}^{-1} \times \frac{539}{279}\; \text{hour} \\ &\approx 105\; \text{mile} \end{aligned}.

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