A pendulum, consisting of a ball of mass m = 0.5 kg attached to the end of a mas

Question

A pendulum, consisting of a ball of mass m = 0.5 kg attached to the end of a massless cord of length l = 0.75 m, can swing vertically about the upper end which is fixed. The ball is pulled aside to an angle of 0 = 30 from the vertical and released from rest. (a) What is the speed of the ball at the lowest point? (b) Does this speed increase, decrease, or remain the same if the angle 0 is increased?

A. A pendulum, consisting of a ball of mass m 0.5 kg attached to the end of a massless cord of length 0.75 m, can swing vertically about the upper end which is fixed. The ball is pulled aside to an angle of = 30° from the vertical and released from rest. (a) What is the speed of the ball at the lowest point? (b) Does this speed increase, decrease, or remain the same if the angle is increased? B. A 500 g block is released from rest at a height yo above a vertical spring with spring constant k = 400 N/m and negligible mass. The block sticks to the spring and mom entarily stops after compressing the spring 18.0 cm. How much work is done (a) by the block on the spring, (b) by the spring on the block? (c) What is the value of yo? (d) If the block were released from the height 1.5yo above the spring, what would be the maximum compression of the spring?

Explanation / Answer

A)The speed at the lowest point will be:

v = sqrt (2 g h)

h = L (1 - cos(theta))

v = sqrt [2 x g x L (1 - cos(theta))]

v = sqrt [2 x 9.81 x 0.75(1 - cos30)] = 1.404 m/s

Hence, v = 1.404 m/s

(b)As we saw in the former part

v varies with cos of the angle, with the increase of the angle the value of cos(angle) reduces, so the quantity (1 - cos(theta)) increases and hence speed will increase.

Hence, speed increases with increase of angle.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.