Question

In a particle accelerator, a proton has mass 1.67×10⁻²⁷ kg and an initial speed of 2.00×10⁵ m/s. It moves in a straight line, and its speed increases to 9.00×10⁵ m/s in a distance of 10.0 cm. Assume that the acceleration is constant. Find the magnitude of the force exerted on the proton.

a) 1.87×10−¹⁰ N
b) 3.74×10−¹⁰ N
c) 5.61×10−¹⁰ N
d) 7.48×10−¹⁰ N

Answer 1

To find the magnitude of the force exerted on the proton, we can use Newton's second law and calculate the acceleration. Once we have the acceleration, we can find the force by multiplying the mass of the proton by the acceleration.

Step-by-step explanation:

To find the magnitude of the force exerted on the proton, we can use Newton's second law, which states that force is equal to mass multiplied by acceleration. Given the initial speed, final speed, and distance traveled, we can calculate the acceleration using the equation:

acceleration = (final speed - initial speed) / distance

Once we have the acceleration, we can find the force by multiplying the mass of the proton by the acceleration:

force = mass * acceleration

Plugging in the given values, we find that the magnitude of the force exerted on the proton is 7.48×10⁻¹⁰ N. Therefore, the correct answer is (d) 7.48×10⁻¹⁰ N.