Question

a 2.0 kg pendulum bob swings on a 2.0-m-long string. the bob's speed is 1.5 m/s when the string makes a 15 degree angle with vertical and the bob is moving toward the bottom of the arc. at this instant, what are the magnitudes of a. the bob's tangential acceleration b. the bob's radial acceleration, and c. the tension in the string?

Answer 1

To find the bob's tangential acceleration, we can use the formula a_t = r * alpha. The bob's radial acceleration can be calculated using the formula a_r = omega^2 * r. To find the tension in the string, we can use the formula T = m * (a_t + a_r).

Step-by-step explanation:

To find the bob's tangential acceleration, we can use the formula:

at = r × α

where r is the radius and α is the angular acceleration. We can find the angular acceleration using:

α = ω2 / r

where ω is the angular velocity. The tangential acceleration is the component of acceleration in the direction of motion, so the magnitude is equal to the angular acceleration. Therefore, the bob's tangential acceleration is the same as its angular acceleration.

The bob's radial acceleration can be calculated using the formula:

ar = ω2 × r

where ω is the angular velocity and r is the radius.

To find the tension in the string, we can use the formula:

T = m × (at + ar)

where T is the tension, m is the mass, at is the tangential acceleration, and ar is the radial acceleration.