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3 years ago

What is the mass of a cart that accelerates at 3.0 m/s if a 0.5 N force is applied?

Physics

1 answer:

frozen [14]3 years ago

6 0

The mass of the cart is 0.167 kg

Explanation:

We can solve the problem by using Newton's second law, which states that the net force applied to an object is equal to the product between its mass and its acceleration:

$F=ma$

where

F is the net force acting on an object

m is its mass

a is its acceleration

For the cart in this problem, we have

F = 0.5 N is the net force applied

$a=3.0 m/s^2$ is the acceleration

Substituting, we find the mass:

$m=\frac{F}{a}=\frac{0.5}{3.0}=0.167 kg$

Learn more about Newton's second law:

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A thermometer initially reading 212F is placed in a room where the temperature is 70F. After 2 minutes the thermometer reads 125

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Answer:

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Explanation:

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T∞ be the temperature of the room = 70°F

T₀ be the initial temperature of the thermometer = 212°F

And m, c, h are all constants from the cooling law relation

From Newton's law of cooling

Rate of Heat loss by the cake = Rate of Heat gain by the environment

- mc (d/dt)(T - T∞) = h (T - T∞)

(d/dt) (T - T∞) = dT/dt (Because T∞ is a constant)

dT/dt = (-h/mc) (T - T∞)

Let (h/mc) be k

dT/(T - T∞) = -kdt

Integrating the left hand side from T₀ to T and the right hand side from 0 to t

In [(T - T∞)/(T₀ - T∞)] = -kt

(T - T∞)/(T₀ - T∞) = e⁻ᵏᵗ

(T - T∞) = (T₀ - T∞)e⁻ᵏᵗ

Inserting the known variables

(T - 70) = (212 - 70)e⁻ᵏᵗ

(T - 70) = 142 e⁻ᵏᵗ

At t = 2 minute, T = 125°F

125 - 70 = 142 e⁻ᵏᵗ

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- k(2) = - 0.9485

k = 0.4742 /min

At time t = 4 mins

kt = 0.4742 × 4 = 1.897

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