Question

A device has a 100-g wooden shuttle that is pulled horizontally along a fixed frictionless wooden rail by an elastic band. The shuttle is released when the elastic band has 6.4 N tension at a 35° angle. What is the magnitude of the initial acceleration of the shuttle?

Answer 1

Answer:

52.4 m/s^2

Explanation:

First of all, we have to calculate the horizontal component of the force exerted by the elastic band, which is the force that acts on the device:

$F_x = F cos \theta = (6.4 N)(cos 35^{\circ})=5.24 N$

So now, by using Newton's second Law:

$F_x = ma$

We can calculate the initial acceleration of the shuttle (mass: m=100 g=0.1 kg):

$a=\frac{F_x}{m}=\frac{5.24 N}{0.1 kg}=52.4 m/s^2$

Answer 2

The acceleration of the shuttle is 52.4 m/s².

Horizontal component of the force

The horizontal component of the force exerted is calculated as follows;

Fₓ = Fcos(θ)

Fₓ = 6.4 x cos(35)

Fₓ = 5.24 N

Acceleration of the shuttle

The acceleration of the shuttle is calculated as follows;

$a = \frac{F_x}{m} \\\\a = \frac{5.24}{0.1} \\\\a = 52.4 \ m/s^2$

Thus, the acceleration of the shuttle is 52.4 m/s².

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