As we will see in this example, when the mass of an object is small, even modest

Question

As we will see in this example, when the mass of an object is small, even modest forces can cause very large accelerations. In a color TV picture tube, an electric field exerts a net force with magnitude 1.60 Times 10^-13 N on an electron (m = 9.11 Times 10^-31 kg). What is the electron's acceleration? (Figure 1) shows our simple diagram. The statement of the problem tells us that the net force on the electron is due to the electric field, so we consider only the electric-field force. (If other forces act on the electron, they are negligible or sum to zero.) The direction of the acceleration must be the same as that of the force; we designate this as the +x direction. SOLVE We use Newton's second law in component form, rearranging it slightly to solve for acceleration: a_x = sigma F_x/m = 1.60 Times 10^-13 N/9.11 Times 10^-31 kg = 1.60 Times 10^-13 kg middot m/s^2/9.11 Times 10^-31 kg Notice that the magnitudes of these quantities are far outside the range of everyday experience. Because the mass of the electron is minuscule, a tiny force produces a huge acceleration. If the electric field exerted the same net force on a proton (m = 1.67 Times 10^-27 kg), how long would it take for the proton to travel 0.45 m within the field if it started from rest? Express your answer in seconds to three significant figures.

Explanation / Answer

Part A)

F = force exerted = 1.6 x 10-13 N

m = mass of proton = 1.67 x 10-31 kg

a = acceleration = F/m = (1.6 x 10-13 ) / (1.67 x 10-31) = 9.6 x 1017 m/s2

Vo = initial speed = 0 m/s

X = displacement = 0.45 m
t = time taken

using the equation

X = Vo t + (0.5) a t2

0.45 = 0 (t) + (0.5) (9.6 x 1017) t2

t = 9.7 x 10-10 sec

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