A car sitting at rest is hit from the rear by a semi-trailer truck moving at 13

Question

A car sitting at rest is hit from the rear by a semi-trailer truck moving at 13 m/s . The car lurches forward with an acceleration of about 270 m/ s 2 . An arrow shown in (Figure 1) represents the force that the neck muscle exerts on the head so that it accelerates forward with the body instead of flipping backward. The head has a mass of 4.9 kg . What is the horizontal component of the force F required to cause this head acceleration? Express your answer to two significant figures and include the appropriate units. If F is directed 37 below the horizontal, what is the magnitude of F ? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

given

ax = 270 m/s^2
m = 4.9 kg

use Newton's second law

Fx = m*ax

F*cos(37) = m*ax

F = m*ax/cos(37)

= 4.9*270/cos(37)

= 1.6*10^3 N

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